The Fundamental Counting Principle & Permutations
|
|
- Randell Jacobs
- 5 years ago
- Views:
Transcription
1 The Fundamental Counting Principle & Permutations POD: You have 7 boxes and 10 balls. You put the balls into the boxes. How many boxes have more than one ball?
2 Why do you use a fundamental counting principal? What operation do you use for fundamental counting principals? What is a permutation? What is the formula for n P r? What is the formula for permutations with repetition?
3 The Fundamental Counting Principle If you have 2 events: 1 event can occur m ways and another event can occur n ways, then the number of ways that both can occur is m*n Event 1 = 4 types of meats Event 2 = 3 types of bread How many different types of sandwiches can you make? 4*3 = 12
4 3 or more events: 3 events can occur m, n, & p ways, then the number of ways all three can occur is m*n*p 4 meats 3 cheeses 3 breads How many different sandwiches can you make? 4*3*3 = 36 sandwiches
5 At a restaurant at Cedar Point, you have the choice of 8 different entrees, 2 different salads, 12 different drinks, & 6 different deserts. How many different dinners (one choice of each) can you choose? 8*2*12*6= 1152 different dinners
6 Fund. Counting Principle with repetition Ohio Licenses plates have 3 # s followed by 3 letters. 1. How many different licenses plates are possible if digits and letters can be repeated? There are 10 choices for digits and 26 choices for letters. 10*10*10*26*26*26= 17,576,000 different plates
7 How many plates are possible if digits and numbers cannot be repeated? There are still 10 choices for the 1 st digit but only 9 choices for the 2 nd, and 8 for the 3 rd. For the letters, there are 26 for the first, but only 25 for the 2 nd and 24 for the 3 rd. 10*9*8*26*25*24= 11,232,000 plates
8 Phone numbers How many different 7 digit phone numbers are possible if the 1 st digit cannot be a 0 or 1? 8*10*10*10*10*10*10= 8,000,000 different numbers
9 Testing A multiple choice test has 10 questions with 4 answers each. How many ways can you complete the test? 4*4*4*4*4*4*4*4*4*4 = 4 10 = 1,048,576
10 Using Permutations An ordering of n objects is a permutation of the objects.
11 There are 6 permutations of the letters A, B, &C ABC ACB BAC BCA CAB CBA You can use the Fund. Counting Principal to determine the number of permutations of n objects. Like this ABC. There are 3 choices for 1 st # 2 choices for 2 nd # 1 choice for 3 rd. 3*2*1 = 6 ways to arrange the letters
12 In general, the # of permutations of n objects is: n! = n*(n-1)*(n-2)*
13 12 skiers How many different ways can 12 skiers in the Olympic finals finish the competition? (if there are no ties) 12! = 12*11*10*9*8*7*6*5*4*3*2*1 = 479,001,600 different ways
14 Factorial with a calculator: Hit math then over, over, over. Option 4
15
16 Back to the finals in the Olympic skiing competition. How many different ways can 3 of the skiers finish 1 st, 2 nd, & 3 rd (gold, silver, bronze) Any of the 12 skiers can finish 1 st, the any of the remaining 11 can finish 2 nd, and any of the remaining 10 can finish 3 rd. So the number of ways the skiers can win the medals is 12*11*10 = 1320
17 Introduction to Permutations y/v/permutations
18 Permutation of n objects taken r at a time n P r =
19 Back to the last problem with the skiers It can be set up as the number of permutations of 12 objects taken 3 at a time. 12 P 3 = 12! = 12! = (12-3)! 9! 12*11*10*9*8*7*6*5*4*3*2*1 = 12*11*10 = *8*7*6*5*4*3*2*1
20 10 colleges, you want to visit all or some. How many ways can you visit 6 of them: Permutation of 10 objects taken 6 at a time: 10 P 6 = 10!/(10-6)! = 10!/4! = 3,628,800/24 = 151,200
21 How many ways can you visit all 10 of them: 10 P 10 = ( 0! By definition = 1) 10!/(10-10)! = 10!/0!= 10! = 3,628,800
22 So far in our problems, we have used distinct objects. If some of the objects are repeated, then some of the permutations are not distinguishable. There are 6 ways to order the letters M,O,M MOM, OMM, MMO MOM, OMM, MMO Only 3 are distinguishable. 3!/2! = 6/2 = 3
23 Permutations with Repetition The number of DISTINGUISHABLE permutations of n objects where one object is repeated q 1 times, another is repeated q 2 times, and so on :
24 Find the number of distinguishable permutations of the letters: OHIO : 4 letters with 0 repeated 2 times 4! 2! = 24 2 = 12 MISSISSIPPI : 11 letters with I repeated 4 times, S repeated 4 times, P repeated 2 times 11! = 4!*4!*2! 39,916,800 = 24*24*2 34,650
25 Find the number of distinguishable permutations of the letters: SUMMER : 360 WATERFALL : 90,720
26 A dog has 8 puppies, 3 male and 5 female. How many birth orders are possible 8!/(3!*5!) = 56
27 Why do you use a fundamental counting principal? To count the number of possibilities of the given conditions. What operation do you use for fundamental counting principals? Multiplication What is a permutation? An ordering of objects. What is the formula for n P r? What is the formula for permutations with repetition?
28 Assignment worksheet
12.1 The Fundamental Counting Principle and Permutations
12.1 The Fundamental Counting Principle and Permutations The Fundamental Counting Principle Two Events: If one event can occur in ways and another event can occur in ways then the number of ways both events
More information19.2 Permutations and Probability
Name Class Date 19.2 Permutations and Probability Essential Question: When are permutations useful in calculating probability? Resource Locker Explore Finding the Number of Permutations A permutation is
More informationMath Steven Noble. November 22nd. Steven Noble Math 3790
Math 3790 Steven Noble November 22nd Basic ideas of combinations and permutations Simple Addition. If there are a varieties of soup and b varieties of salad then there are a + b possible ways to order
More informationTImath.com. Statistics. Too Many Choices!
Too Many Choices! ID: 11762 Time required 40 minutes Activity Overview In this activity, students will investigate the fundamental counting principle, permutations, and combinations. They will find the
More informationWelcome! Worksheet Counting Principal, Permutations, Combinations. Updates: U4T is 12/12
Welcome! U4H1: Worksheet Counting Principal, Permutations, Combinations Updates: U4T is 12/12 Announcement: December 16 th is the last day I will accept late work. No new assignment list since this section
More informationObjectives: Permutations. Fundamental Counting Principle. Fundamental Counting Principle. Fundamental Counting Principle
and Objectives:! apply fundamental counting principle! compute permutations! compute combinations HL2 Math - Santowski! distinguish permutations vs combinations can be used determine the number of possible
More informationWe introduced the Counting Principle earlier in the chapter.
Section 4.6: The Counting Principle and Permutations We introduced the Counting Principle earlier in the chapter. Counting Principle: If a first experiment can be performed in M distinct ways and a second
More informationMath 1116 Probability Lecture Monday Wednesday 10:10 11:30
Math 1116 Probability Lecture Monday Wednesday 10:10 11:30 Course Web Page http://www.math.ohio state.edu/~maharry/ Chapter 15 Chances, Probabilities and Odds Objectives To describe an appropriate sample
More informationPermutations And Combinations Questions Answers
We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with permutations and combinations
More informationFundamental Counting Principle
Lesson 88 Probability with Combinatorics HL2 Math - Santowski Fundamental Counting Principle Fundamental Counting Principle can be used determine the number of possible outcomes when there are two or more
More informationCase 1: If Denver is the first city visited, then the outcome looks like: ( D ).
2.37. (a) Think of each city as an object. Each one is distinct. Therefore, there are 6! = 720 different itineraries. (b) Envision the process of selecting an itinerary as a random experiment with sample
More informationCH 13. Probability and Data Analysis
11.1: Find Probabilities and Odds 11.2: Find Probabilities Using Permutations 11.3: Find Probabilities Using Combinations 11.4: Find Probabilities of Compound Events 11.5: Analyze Surveys and Samples 11.6:
More informationPre-Calculus Semester 1
Pre-Calculus Semester 1 Created By: Jennifer Suby and Kay Knutson Oswego East High School Fall 2015 Sequences & Series 1 2 Sequences and Series Day 1 Notes: Arithmetic Sequences Sequences Sequence: a function
More informationElementary Combinatorics
184 DISCRETE MATHEMATICAL STRUCTURES 7 Elementary Combinatorics 7.1 INTRODUCTION Combinatorics deals with counting and enumeration of specified objects, patterns or designs. Techniques of counting are
More informationIn this section, we will learn to. 1. Use the Multiplication Principle for Events. Cheesecake Factory. Outback Steakhouse. P.F. Chang s.
Section 10.6 Permutations and Combinations 10-1 10.6 Permutations and Combinations In this section, we will learn to 1. Use the Multiplication Principle for Events. 2. Solve permutation problems. 3. Solve
More informationHow can I count arrangements?
10.3.2 How can I count arrangements? Permutations There are many kinds of counting problems. In this lesson you will learn to recognize problems that involve arrangements. In some cases outcomes will be
More informationPermutations. and. Combinations
Permutations and Combinations Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another independent event has n possible outcomes, then there
More informationA counting problem is a problem in which we want to count the number of objects in a collection or the number of ways something occurs or can be
A counting problem is a problem in which we want to count the number of objects in a collection or the number of ways something occurs or can be done. At a local restaurant, for a fixed price one can buy
More informationMTH 245: Mathematics for Management, Life, and Social Sciences
1/1 MTH 245: Mathematics for Management, Life, and Social Sciences Sections 5.5 and 5.6. Part 1 Permutation and combinations. Further counting techniques 2/1 Given a set of n distinguishable objects. Definition
More informationExercises Exercises. 1. List all the permutations of {a, b, c}. 2. How many different permutations are there of the set {a, b, c, d, e, f, g}?
Exercises Exercises 1. List all the permutations of {a, b, c}. 2. How many different permutations are there of the set {a, b, c, d, e, f, g}? 3. How many permutations of {a, b, c, d, e, f, g} end with
More informationStrings. A string is a list of symbols in a particular order.
Ihor Stasyuk Strings A string is a list of symbols in a particular order. Strings A string is a list of symbols in a particular order. Examples: 1 3 0 4 1-12 is a string of integers. X Q R A X P T is a
More informationBayes stuff Red Cross and Blood Example
Bayes stuff Red Cross and Blood Example 42% of the workers at Motor Works are female, while 67% of the workers at City Bank are female. If one of these companies is selected at random (assume a 50-50 chance
More informationPrinciples of Counting
Name Date Principles of Counting Objective: To find the total possible number of arrangements (ways) an event may occur. a) Identify the number of parts (Area Codes, Zip Codes, License Plates, Password,
More informationFundamental. If one event can occur m ways and another event can occur n ways, then the number of ways both events can occur is:.
12.1 The Fundamental Counting Principle and Permutations Objectives 1. Use the fundamental counting principle to count the number of ways an event can happen. 2. Use the permutations to count the number
More informationPermutations and Combinations
Smart Notes.notebook Discrete Math is concerned with counting. Ted TV:How many ways can you arrange a deck of cards? Yannay Khaikin http://ed.ted.com/lessons/how many ways can you arrange a deck of cardsyannay
More informationMathematics Probability: Combinations
a place of mind F A C U L T Y O F E D U C A T I O N Department of Curriculum and Pedagogy Mathematics Probability: Combinations Science and Mathematics Education Research Group Supported by UBC Teaching
More informationCourse Learning Outcomes for Unit V
UNIT V STUDY GUIDE Counting Reading Assignment See information below. Key Terms 1. Combination 2. Fundamental counting principle 3. Listing 4. Permutation 5. Tree diagrams Course Learning Outcomes for
More informationCHAPTER 8 Additional Probability Topics
CHAPTER 8 Additional Probability Topics 8.1. Conditional Probability Conditional probability arises in probability experiments when the person performing the experiment is given some extra information
More informationW = {Carrie (U)nderwood, Kelly (C)larkson, Chris (D)aughtry, Fantasia (B)arrino, and Clay (A)iken}
UNIT V STUDY GUIDE Counting Course Learning Outcomes for Unit V Upon completion of this unit, students should be able to: 1. Apply mathematical principles used in real-world situations. 1.1 Draw tree diagrams
More informationPermutations, Combinations and The Binomial Theorem. Unit 9 Chapter 11 in Text Approximately 7 classes
Permutations, Combinations and The Binomial Theorem Unit 9 Chapter 11 in Text Approximately 7 classes In this unit, you will be expected to: Solve problems that involve the fundamental counting principle.
More informationCOUNTING AND PROBABILITY
CHAPTER 9 COUNTING AND PROBABILITY Copyright Cengage Learning. All rights reserved. SECTION 9.2 Possibility Trees and the Multiplication Rule Copyright Cengage Learning. All rights reserved. Possibility
More informationGeneralized Permutations and The Multinomial Theorem
Generalized Permutations and The Multinomial Theorem 1 / 19 Overview The Binomial Theorem Generalized Permutations The Multinomial Theorem Circular and Ring Permutations 2 / 19 Outline The Binomial Theorem
More informationJessica Fauser EDUC 352 October 21, 2011 Unit Lesson Plan #3. Lesson: Permutations and Combinations Length: 45 minutes Age/Grade Intended: Algebra II
Jessica Fauser EDUC 352 October 21, 2011 Unit Lesson Plan #3 Lesson: Permutations and Combinations Length: 45 minutes Age/Grade Intended: Algebra II Academic Standard(s): A2.8.4 Use permutations, combinations,
More informationConcepts. Materials. Objective
. Activity 14 Let Us Count the Ways! Concepts Apply the multiplication counting principle Find the number of permutations in a data set Find the number of combinations in a data set Calculator Skills Factorial:
More informationSec 4.4. Counting Rules. Bluman, Chapter 4
Sec 4.4 Counting Rules A Question to Ponder: A box contains 3 red chips, 2 blue chips and 5 green chips. A chip is selected, replaced and a second chip is selected. Display the sample space. Do you think
More informationChapter 10A. a) How many labels for Product A are required? Solution: ABC ACB BCA BAC CAB CBA. There are 6 different possible labels.
Chapter 10A The Addition rule: If there are n ways of performing operation A and m ways of performing operation B, then there are n + m ways of performing A or B. Note: In this case or means to add. Eg.
More informationName: 1. Match the word with the definition (1 point each - no partial credit!)
Chapter 12 Exam Name: Answer the questions in the spaces provided. If you run out of room, show your work on a separate paper clearly numbered and attached to this exam. SHOW ALL YOUR WORK!!! Remember
More informationPermutations and Combinations
Permutations and Combinations NAME: 1.) There are five people, Abby, Bob, Cathy, Doug, and Edgar, in a room. How many ways can we line up three of them to receive 1 st, 2 nd, and 3 rd place prizes? The
More informationGrade 6 Math Circles March 9, 2011 Combinations
1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 6 Math Circles March 9, 2011 Combinations Review 1. Evaluate 6! 6 5 3 2 1 = 720 2. Evaluate 5! 7
More informationDay 1 Counting Techniques
Day 1 Counting Techniques Packet p. 1-2 Day 1 Fundamental Counting Principle Other Counting Techniques Notes p. 1 I. Introduction Probability Defined: What do you know about probability? Notes p. 1 I.
More informationCounting Things. Tom Davis March 17, 2006
Counting Things Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles March 17, 2006 Abstract We present here various strategies for counting things. Usually, the things are patterns, or
More informationAdditional Topics in Probability and Counting. Try It Yourself 1. The number of permutations of n distinct objects taken r at a time is
168 CHAPTER 3 PROBABILITY 3.4 Additional Topics in Probability and Counting WHAT YOU SHOULD LEARN How to find the number of ways a group of objects can be arranged in order How to find the number of ways
More information6/24/14. The Poker Manipulation. The Counting Principle. MAFS.912.S-IC.1: Understand and evaluate random processes underlying statistical experiments
The Poker Manipulation Unit 5 Probability 6/24/14 Algebra 1 Ins1tute 1 6/24/14 Algebra 1 Ins1tute 2 MAFS. 7.SP.3: Investigate chance processes and develop, use, and evaluate probability models MAFS. 7.SP.3:
More informationUNIT 2. Counting Methods
UNIT 2 Counting Methods IN THIS UNIT, YOU WILL BE EXPECTED TO: Solve problems that involve the fundamental counting principle. Solve problems that involve permutations. Solve problems that involve combinations.
More informationSec. 4.2: Introducing Permutations and Factorial notation
Sec. 4.2: Introducing Permutations and Factorial notation Permutations: The # of ways distinguishable objects can be arranged, where the order of the objects is important! **An arrangement of objects in
More informationFinite Math B, Chapter 8 Test Review Name
Finite Math B, Chapter 8 Test Review Name Evaluate the factorial. 1) 6! A) 720 B) 120 C) 360 D) 1440 Evaluate the permutation. 2) P( 10, 5) A) 10 B) 30,240 C) 1 D) 720 3) P( 12, 8) A) 19,958,400 B) C)
More informationSTAT 430/510 Probability
STAT 430/510 Probability Hui Nie Lecture 1 May 26th, 2009 Introduction Probability is the study of randomness and uncertainty. In the early days, probability was associated with games of chance, such as
More informationPermutations and Combinations. Quantitative Aptitude & Business Statistics
Permutations and Combinations Statistics The Fundamental Principle of If there are Multiplication n 1 ways of doing one operation, n 2 ways of doing a second operation, n 3 ways of doing a third operation,
More informationPermutations and Combinations. MATH 107: Finite Mathematics University of Louisville. March 3, 2014
Permutations and Combinations MATH 107: Finite Mathematics University of Louisville March 3, 2014 Multiplicative review Non-replacement counting questions 2 / 15 Building strings without repetition A familiar
More informationGrade 6 Math Circles Winter February 10/11 Counting
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles Winter 2015 - February 10/11 Counting What is Counting? When you think of the word
More informationApril 10, ex) Draw a tree diagram of this situation.
April 10, 2014 12-1 Fundamental Counting Principle & Multiplying Probabilities 1. Outcome - the result of a single trial. 2. Sample Space - the set of all possible outcomes 3. Independent Events - when
More informationMath 14 Lecture Notes Ch. 3.6
Math Lecture Notes h... ounting Rules xample : Suppose a lottery game designer wants to list all possible outcomes of the following sequences of events: a. tossing a coin once and rolling a -sided die
More information6.4 Permutations and Combinations
Math 141: Business Mathematics I Fall 2015 6.4 Permutations and Combinations Instructor: Yeong-Chyuan Chung Outline Factorial notation Permutations - arranging objects Combinations - selecting objects
More information1. Write the first five terms of the sequence with 0 3 and. 2. Write an explicit rule and a recursive rule for the sequence.
LESSON 12.1 Name.Date Warm-Up Exercises For use before Lesson 12.1, pages 701-707 Avnilnbic as a tr«ms(iarency Evaluate. 1. 3! 2. 7! 4! 4. 10! (10-4)! Daily Homework Quiz For use after Lesson 11.5, pages
More informationExamples: Experiment Sample space
Intro to Probability: A cynical person once said, The only two sure things are death and taxes. This philosophy no doubt arose because so much in people s lives is affected by chance. From the time a person
More informationUnit 14 Probability. Target 3 Calculate the probability of independent and dependent events (compound) AND/THEN statements
Target 1 Calculate the probability of an event Unit 14 Probability Target 2 Calculate a sample space 14.2a Tree Diagrams, Factorials, and Permutations 14.2b Combinations Target 3 Calculate the probability
More informationQuestion 1: How do you count choices using the multiplication principle?
8.1 Permutations Question 1: How do you count choices using the multiplication principle? Question 2: What is factorial notation? Question 3: What is a permutation? In Chapter 7, we focused on using statistics
More informationUnit 2 Lesson 2 Permutations and Combinations
Unit 2 Lesson 2 Permutations and Combinations Permutations A permutation is an arrangement of objects in a definite order. The number of permutations of n distinct objects is n! Example: How many permutations
More informationLearning Objectives for Section 7.4 Permutations and Combinations. 7.4 Permutations and Combinations
Learning Objectives for Section 7.4 Permutations and Combinations The student will be able to set up and compute factorials. The student will be able to apply and calculate permutations. The student will
More informationSection : Combinations and Permutations
Section 11.1-11.2: Combinations and Permutations Diana Pell A construction crew has three members. A team of two must be chosen for a particular job. In how many ways can the team be chosen? How many words
More information* Order Matters For Permutations * Section 4.6 Permutations MDM4U Jensen. Part 1: Factorial Investigation
Section 4.6 Permutations MDM4U Jensen Part 1: Factorial Investigation You are trying to put three children, represented by A, B, and C, in a line for a game. How many different orders are possible? a)
More informationGrade 7/8 Math Circles November 8 & 9, Combinatorial Counting
Faculty of Mathematics Waterloo, Ontario NL G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles November 8 & 9, 016 Combinatorial Counting Learning How to Count (In a New Way!)
More informationMAT104: Fundamentals of Mathematics II Summary of Counting Techniques and Probability. Preliminary Concepts, Formulas, and Terminology
MAT104: Fundamentals of Mathematics II Summary of Counting Techniques and Probability Preliminary Concepts, Formulas, and Terminology Meanings of Basic Arithmetic Operations in Mathematics Addition: Generally
More informationProbability. 4-6 Counting. Fundamental Counting Rule Permutations Combinations
Probability 4-6 Counting Fundamental Counting Rule Permutations Combinations Fundamental Counting Rule (Space Rule) For a sequence of two or more events m and n The first event occurs m ways and the second
More informationAlgebra II Probability and Statistics
Slide 1 / 241 Slide 2 / 241 Algebra II Probability and Statistics 2016-01-15 www.njctl.org Slide 3 / 241 Table of Contents click on the topic to go to that section Sets Independence and Conditional Probability
More informationFundamental Counting Principle 2.1 Page 66 [And = *, Or = +]
Math 3201 Assignment 1 of 1 Unit 2 Counting Methods Name: Fundamental Counting Principle 2.1 Page 66 [And = *, Or = +] Identify the choice that best completes the statement or answers the question. 1.
More informationProbability. The MEnTe Program Math Enrichment through Technology. Title V East Los Angeles College
Probability The MEnTe Program Math Enrichment through Technology Title V East Los Angeles College 2003 East Los Angeles College. All rights reserved. Topics Introduction Empirical Probability Theoretical
More informationFinite Mathematics MAT 141: Chapter 8 Notes
Finite Mathematics MAT 4: Chapter 8 Notes Counting Principles; More David J. Gisch The Multiplication Principle; Permutations Multiplication Principle Multiplication Principle You can think of the multiplication
More informationCS1800: Permutations & Combinations. Professor Kevin Gold
CS1800: Permutations & Combinations Professor Kevin Gold Permutations A permutation is a reordering of something. In the context of counting, we re interested in the number of ways to rearrange some items.
More informationProbability. Engr. Jeffrey T. Dellosa.
Probability Engr. Jeffrey T. Dellosa Email: jtdellosa@gmail.com Outline Probability 2.1 Sample Space 2.2 Events 2.3 Counting Sample Points 2.4 Probability of an Event 2.5 Additive Rules 2.6 Conditional
More informationAlgebra II. Slide 1 / 241. Slide 2 / 241. Slide 3 / 241. Probability and Statistics. Table of Contents click on the topic to go to that section
Slide 1 / 241 Slide 2 / 241 Algebra II Probability and Statistics 2016-01-15 www.njctl.org Table of Contents click on the topic to go to that section Slide 3 / 241 Sets Independence and Conditional Probability
More informationMATH STUDENT BOOK. 8th Grade Unit 10
MATH STUDENT BOOK 8th Grade Unit 10 Math 810 Probability Introduction 3 1. Outcomes 5 Tree Diagrams and the Counting Principle 5 Permutations 12 Combinations 17 Mixed Review of Outcomes 22 SELF TEST 1:
More informationData Analysis. (1) Page #16 34 Column, Column (Skip part B), and #57 (A S/S)
H Algebra 2/Trig Unit 9 Notes Packet Name: Period: # Data Analysis (1) Page 663 664 #16 34 Column, 45 54 Column (Skip part B), and #57 (A S/S) (2) Page 663 664 #17 32 Column, 46 56 Column (Skip part B),
More informationPrecalc Unit 10 Review
Precalc Unit 10 Review Name: Use binomial expansion to expand. 1. 2. 3.. Use binomial expansion to find the term you are asked for. 4. 5 th term of (4x-3y) 8 5. 3 rd term of 6. 4 th term of 7. 2 nd term
More informationUnit 5 Radical Functions & Combinatorics
1 Graph of y Unit 5 Radical Functions & Combinatorics x: Characteristics: Ex) Use your knowledge of the graph of y x and transformations to sketch the graph of each of the following. a) y x 5 3 b) f (
More informationFundamental Counting Principle 2.1 Page 66 [And = *, Or = +]
Math 3201 Assignment 2 Unit 2 Counting Methods Name: Fundamental Counting Principle 2.1 Page 66 [And = *, Or = +] Identify the choice that best completes the statement or answers the question. Show all
More informationUnit on Permutations and Combinations (Counting Techniques)
Page 1 of 15 (Edit by Y.M. LIU) Page 2 of 15 (Edit by Y.M. LIU) Unit on Permutations and Combinations (Counting Techniques) e.g. How many different license plates can be made that consist of three digits
More informationAdvanced Intermediate Algebra Chapter 12 Summary INTRO TO PROBABILITY
Advanced Intermediate Algebra Chapter 12 Summary INTRO TO PROBABILITY 1. Jack and Jill do not like washing dishes. They decide to use a random method to select whose turn it is. They put some red and blue
More information* Order Matters For Permutations * Section 4.6 Permutations MDM4U Jensen. Part 1: Factorial Investigation
Section 4.6 Permutations MDM4U Jensen Part 1: Factorial Investigation You are trying to put three children, represented by A, B, and C, in a line for a game. How many different orders are possible? a)
More information3 ky. t x 1) 1/3, -1/2 2) = 140 4) 74 units 5) a) 2400 b) $12 c) 96 students. 6) a) y = 1.10x x b) points c) 1984, 2003
1) 1/3, -1/2 2) 3.8039 3) m SRQ < = 140 4) 74 units 5) a) 2400 b) $12 c) 96 students t x 6) a) y = 1.10x 2 30.49x + 890.03 b) 790.61 points c) 1984, 2003 7) a) 4 3 b) 3ky 3y 3 3 5 7 4 4 3 ky 8) 10) a)
More information19.2 Permutations and Probability Combinations and Probability.
19.2 Permutations and Probability. 19.3 Combinations and Probability. Use permutations and combinations to compute probabilities of compound events and solve problems. When are permutations useful in calculating
More informationLESSON 4 COMBINATIONS
LESSON 4 COMBINATIONS WARM UP: 1. 4 students are sitting in a row, and we need to select 3 of them. The first student selected will be the president of our class, the 2nd one selected will be the vice
More informationCh 9.6 Counting, Permutations, and Combinations LESSONS
Ch 9.6 Counting, Permutations, and Combinations SKILLS OBJECTIVES Apply the fundamental counting principle to solve counting problems. Apply permutations to solve counting problems. Apply combinations
More informationProbability and Counting Techniques
Probability and Counting Techniques Diana Pell (Multiplication Principle) Suppose that a task consists of t choices performed consecutively. Suppose that choice 1 can be performed in m 1 ways; for each
More informationProbability Concepts and Counting Rules
Probability Concepts and Counting Rules Chapter 4 McGraw-Hill/Irwin Dr. Ateq Ahmed Al-Ghamedi Department of Statistics P O Box 80203 King Abdulaziz University Jeddah 21589, Saudi Arabia ateq@kau.edu.sa
More informationProbability Warm-Up 1 (Skills Review)
Probability Warm-Up 1 (Skills Review) Directions Solve to the best of your ability. (1) Graph the line y = 3x 2. (2) 4 3 = (3) 4 9 + 6 7 = (4) Solve for x: 4 5 x 8 = 12? (5) Solve for x: 4(x 6) 3 = 12?
More informationLet s Count the Ways
Overview Activity ID: 8609 Math Concepts Materials Students will be introduced to the different ways to calculate counting principle TI-30XS numbers of outcomes, including using the counting principle.
More informationChapter Permutations and Combinations. Section 4 Permutations and Combinations. Example. Definition of n Factorial (n!)
Chapter 7 Logic, Sets, and Counting Section 4 Permutations and Combinations 7.4 Permutations and Combinations For more complicated problems, we will need to develop two important concepts: permutations
More informationCHAPTER 9 - COUNTING PRINCIPLES AND PROBABILITY
CHAPTER 9 - COUNTING PRINCIPLES AND PROBABILITY Probability is the Probability is used in many real-world fields, such as insurance, medical research, law enforcement, and political science. Objectives:
More informationSTAT 430/510 Probability Lecture 1: Counting-1
STAT 430/510 Probability Lecture 1: Counting-1 Pengyuan (Penelope) Wang May 22, 2011 Introduction In the early days, probability was associated with games of chance, such as gambling. Probability is describing
More informationExamples. 3! = (3)(2)(1) = 6, and 5! = (5)(4)(3)(2)(1) = 120.
Counting I For this section you ll need to know what factorials are. If n N, then n-factorial, which is written as n!, is the roduct of numbers n(n 1)(n )(n 3) (4)(3)()(1) Examles. 3! = (3)()(1) = 6, and!
More informationDistinguishable Boxes
Math 10B with Professor Stankova Worksheet, Discussion #5; Thursday, 2/1/2018 GSI name: Roy Zhao Distinguishable Boxes Examples 1. Suppose I am catering from Yali s and want to buy sandwiches to feed 60
More informationWell, there are 6 possible pairs: AB, AC, AD, BC, BD, and CD. This is the binomial coefficient s job. The answer we want is abbreviated ( 4
2 More Counting 21 Unordered Sets In counting sequences, the ordering of the digits or letters mattered Another common situation is where the order does not matter, for example, if we want to choose a
More informationthe largest sum of three numbers whose faces come together at a corner?
Question 1 The following figure may be folded along the lines shown to form a number cube. What is the largest sum of three numbers whose faces come together at a corner? Question 1 The following figure
More informationSTATISTICAL COUNTING TECHNIQUES
STATISTICAL COUNTING TECHNIQUES I. Counting Principle The counting principle states that if there are n 1 ways of performing the first experiment, n 2 ways of performing the second experiment, n 3 ways
More informationPermutations and Combinations
Permutations and Combinations In statistics, there are two ways to count or group items. For both permutations and combinations, there are certain requirements that must be met: there can be no repetitions
More informationCPCS 222 Discrete Structures I Counting
King ABDUL AZIZ University Faculty Of Computing and Information Technology CPCS 222 Discrete Structures I Counting Dr. Eng. Farag Elnagahy farahelnagahy@hotmail.com Office Phone: 67967 The Basics of counting
More informationUnit 5, Activity 1, The Counting Principle
Unit 5, Activity 1, The Counting Principle Directions: With a partner find the answer to the following problems. 1. A person buys 3 different shirts (Green, Blue, and Red) and two different pants (Khaki
More informationCounting and Probability
0838 ch0_p639-693 0//007 0:3 PM Page 633 CHAPTER 0 Counting and Probability The design below is like a seed puff of a dandelion just before it is dispersed by the wind. The design shows the outcomes from
More informationBusiness Statistics. Chapter 4 Using Probability and Probability Distributions QMIS 120. Dr. Mohammad Zainal
Department of Quantitative Methods & Information Systems Business Statistics Chapter 4 Using Probability and Probability Distributions QMIS 120 Dr. Mohammad Zainal Chapter Goals After completing this chapter,
More information