Aim: How many different ways???
|
|
|
- Valentine Bryan
- 5 years ago
- Views:
Transcription
1 May 14th Aim: How many different ways??? Get Ready: Some books are laid on a desk. Two are English, three are mathematics, one is French, and four are global. Theresa selects an English book and Isabelle then selects a global book. Both girls take their selections to the library to read. If Truman then selects two books at random, what is the probability that he selects an English book or a mathematics book? 1
2 Factorials 6!= 6 * 5 * 4 * 3 * 2 *1 = ! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 *1 = 479,001,600 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040 4! = 8! = 72! = 2
3 How Many Different Ways??? With your partner, take four different colored blocks and complete the activity to see how many different ways you can answer each situation. We will come back together at. 3
4 Mr. Rogers is having a contest for his students who are taking the Integrated Algebra Regents Exam. From everyone who takes the exam, he will randomly select only three students from whoever gets a 95+ on the test to take them out for ice cream and give them a free movie pass. After the exam results come in, Jamie got a 96, Adam got a 96, Trevor got a 97, and Alisa got a 99. Since Mr. Rogers said he can only take 3 students, how many different combinations of students (Jamie, Adam, Trevor, and Alisa) can Mr. Rogers take for ice cream and give a free movie pass? Combinations When arranging n objects into r places when order is not important. ncr = npr r! n: the # of objects you're arranging r: the # of places in your arrangement 8C3 = npr = 8*7*6 = 336 = 56 r! 3*2*1 6 Back to Mr. Rogers... n = r = How to do it on the graphing calculator... Practice: 10C5 = 7C2 = 67C21 = The student council has 6 members, but there is going to be a meeting where only 3 members need to attend. How many different triplets can attend the meeting? There are 14 members on a school's basketball team. In how many ways can the coach pick the starters? (There are 5 starters) 4
5 Stuart is having a race with his four toy cars. He has a blue car, green car, red car, and yellow car that he will release from the top of a ramp that he made. How many different results can Stuart have for which car got in first, second, and third place? Permutations npr = When arranging n objects into r places when order is important. n! (n r)! n: the # of objects you're arranging r: the # of places in your arrangement Back to Stuart n = r = How to do it on the graphing calculator... The shortcut 9P4 =9*8*7*6 = P3 =12 * 11 * 10 = 1320 Do you see it? 8P3 = Practice 10P5 = 15P8 = A class of 21 students elects 4 people to office, a president, a vice president, a secretary and a treasurer. How many different ways can people be elected? If 7 people are in a race, then how many different ways of 1st, 2nd, and 3rd place winners can we have? 5
6 6
7 Recap Key Points Next Class: Due Next Time: 7
8 1. How many different 4 digit numbers can you make from the numbers 2, 5, 8, 3? 2. A lock combination has 5 digits between 0 and 9. How many different combinations are there? 3. Sally has 10 posters, but only wants to hang up 3 of themhow many different ways can she choose the 3? 4. Ten people are running in a race how many different ways can the gold, silver and bronze medals be given out? 5. In how many ways can a boss choose 4 out of his 10 employees to be on a committee? 8
Permutations. 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
Independent Events. If we were to flip a coin, each time we flip that coin the chance of it landing on heads or tails will always remain the same.
Independent Events Independent events are events that you can do repeated trials and each trial doesn t have an effect on the outcome of the next trial. If we were to flip a coin, each time we flip that
7A: I can identify and count the outcomes of an experiment and calculate the theoretical probability of an event.
Geometry ^ t2r0`1c8p QKnuPtha\ esnohfftxwaacrger ililjcs.\ D callklw Jr^iSgDhgtTsD FraeKszerr_vPesdV. Assignment Name ID: 1 Date Period 7A: I can identify and count the outcomes of an experiment and calculate
Counting Principle/ Permutations and Combinations
Counting Principle/ Permutations and Combinations T.S. Demonstrate Understanding of Concept AutoSave 1 1.) Paul has three tops, one red, one green, and one blue. He also has four pairs of pants: one white,
Term 4 Test 3 Graded Assignment 1 Extra Practice
Algebra 2 p l2c0sa5j UKcustTaw WSeozfZtlwzaZr\eh slql^cf.b H OAKlYlc ZriiEgWhotAsb Lrwe\sXenrEvgeOdy. Term 4 Test 3 Graded Assignment Extra Practice State if each scenario involves a permutation or a combination.
Sec. 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
Name: Class: Date: ID: A
Class: Date: Chapter 0 review. A lunch menu consists of different kinds of sandwiches, different kinds of soup, and 6 different drinks. How many choices are there for ordering a sandwich, a bowl of soup,
Probability 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?
19.2 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
Fundamental 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
Practice Quiz - Permutations & Combinations
Algebra 2 Practice Quiz - Permutations & Combinations Name Date Period Determine whether the scenario involves independent or dependent events. Then find the probability. 1) A box of chocolates contains
Day 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.
ATHS FC Math Department Al Ain Remedial worksheet. Lesson 10.4 (Ellipses)
ATHS FC Math Department Al Ain Remedial worksheet Section Name ID Date Lesson Marks Lesson 10.4 (Ellipses) 10.4, 10.5, 0.4, 0.5 and 0.6 Intervention Plan Page 1 of 19 Gr 12 core c 2 = a 2 b 2 Question
Permutations. Used when "ORDER MATTERS"
Date: Permutations Used when "ORDER MATTERS" Objective: Evaluate expressions involving factorials. (AN6) Determine the number of possible arrangements (permutations) of a list of items. (AN8) 1) Mrs. Hendrix,
Unit 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
MATH 13150: Freshman Seminar Unit 4
MATH 1150: Freshman Seminar Unit 1. How to count the number of collections The main new problem in this section is we learn how to count the number of ways to pick k objects from a collection of n objects,
Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN. Mathematics 3201
Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN Mathematics 20 SAMPLE MID-YEAR EXAMINATION #2 January 205 Value: 70 Marks Duration: 2 Hours General Instructions
19.3 Combinations and Probability
Name Class Date 19.3 Combinations and Probability Essential Question: What is the difference between a permutaion and a combination? Explore Finding the Number of Combinations A combination is a selection
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
More 9.-9.3 Practice Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. ) In how many ways can you answer the questions on
Name Date Class Practice A. 1. In how many ways can you arrange the letters in the word NOW? List the permutations.
708 Name Date _ Class _ Practice A Permutations. In how many ways can you arrange the letters in the word NOW? List the permutations. 2. In how many ways can you arrange the numbers 4, 5, 6, and 7 to make
Fundamentals of Probability
Fundamentals of Probability Introduction Probability is the likelihood that an event will occur under a set of given conditions. The probability of an event occurring has a value between 0 and 1. An impossible
April 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
Advanced 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
How is data presented, compared and used to predict future outcomes?
How is data presented, compared and used to predict future outcomes? The standards for this domain MM1D1 Students will determine the number of outcomes related to a given event. MM1D2 Students will use
Date Period State if each scenario involves a permutation or a combination. Then find the number of possibilities. ncr or npr
Algebra 2 G h2y0cic pk_ultta` LSeoxfftrwFaPrXeq qlolkco.p E nalltls jroifgvhztdso mrxeosbe^ravyeddt. Ultimate Probability Name Date Period State if each scenario involves a permutation or a combination.
3 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)
* 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)
Probability Study Guide Date Block
Probability Study Guide Name Date Block In a regular deck of 52 cards, face cards are Kings, Queens, and Jacks. Find the following probabilities, if one card is drawn: 1)P(not King) 2) P(black and King)
Warm Up Need a calculator
Find the length. Round to the nearest hundredth. QR Warm Up Need a calculator 12.9(sin 63 ) = QR 11.49 cm QR Check Homework Objectives Solve problems involving permutations. For a main dish, you can choose
Principles of Mathematics 12: Explained!
www.math12.com 284 Lesson 2, Part One: Basic Combinations Basic combinations: In the previous lesson, when using the fundamental counting principal or permutations, the order of items to be arranged mattered.
Unit 8, Activity 1, Vocabulary Self-Awareness Chart
Unit 8, Activity 1, Vocabulary Self-Awareness Chart Vocabulary Self-Awareness Chart WORD +? EXAMPLE DEFINITION Central Tendency Mean Median Mode Range Quartile Interquartile Range Standard deviation Stem
Objectives: 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
1. Simplify 5! 2. Simplify P(4,3) 3. Simplify C(8,5) ? 6. Simplify 5
Algebra 2 Trig H 11.4 and 11.5 Review Complete the following without a calculator: 1. Simplify 5! 2. Simplify P(4,3) 3. Simplify C(8,5) 4. Solve 12C5 12 C 5. Simplify? nc 2? 6. Simplify 5 P 2 7. Simplify
Permutations & Combinations
Permutations & Combinations Extension 1 Mathematics HSC Revision UOW PERMUTATIONS AND COMBINATIONS: REVIEW 1. A combination lock has 4 dials each with 10 digits. How many possible arrangements are there?
Concepts. 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:
University of Connecticut Department of Mathematics
University of Connecticut Department of Mathematics Math 070Q Exam A Fall 07 Name: TA Name: Discussion: Read This First! This is a closed notes, closed book exam. You cannot receive aid on this exam from
PS 3.8 Probability Concepts Permutations & Combinations
BIG PICTURE of this UNIT: How can we visualize events and outcomes when considering probability events? How can we count outcomes in probability events? How can we calculate probabilities, given different
THE ALGEBRA III MIDTERM EXAM REVIEW Name
THE ALGEBRA III MIDTERM EXAM REVIEW Name This review MUST be turned in when you take the midterm exam OR you will not be allowed to take the midterm and will receive a ZERO for the exam. ALG III Midterm
11.3B Warmup. 1. Expand: 2x. 2. Express the expansion of 2x. using combinations. 3. Simplify: a 2b a 2b
11.3 Warmup 1. Expand: 2x y 4 2. Express the expansion of 2x y 4 using combinations. 3 3 3. Simplify: a 2b a 2b 4. How many terms are there in the expansion of 2x y 15? 5. What would the 10 th term in
* 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)
Chapter 2 Math
Chapter 2 Math 3201 1 Chapter 2: Counting Methods: Solving problems that involve the Fundamental Counting Principle Understanding and simplifying expressions involving factorial notation Solving problems
6.4 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
Algebra II- Chapter 12- Test Review
Sections: Counting Principle Permutations Combinations Probability Name Choose the letter of the term that best matches each statement or phrase. 1. An illustration used to show the total number of A.
Unit 1 Day 1: Sample Spaces and Subsets. Define: Sample Space. Define: Intersection of two sets (A B) Define: Union of two sets (A B)
Unit 1 Day 1: Sample Spaces and Subsets Students will be able to (SWBAT) describe events as subsets of sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions,
In 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
Unit 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
We 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
Principles 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,
4.1 Organized Counting McGraw-Hill Ryerson Mathematics of Data Management, pp
Name 4.1 Organized Counting McGraw-Hill yerson Mathematics of Data Management, pp. 225 231 1. Draw a tree diagram to illustrate the possible travel itineraries for Pietro if he can travel from home to
6. In how many different ways can you answer 10 multiple-choice questions if each question has five choices?
Pre-Calculus Section 4.1 Multiplication, Addition, and Complement 1. Evaluate each of the following: a. 5! b. 6! c. 7! d. 0! 2. Evaluate each of the following: a. 10! b. 20! 9! 18! 3. In how many different
Jump, Frog, Jump. 3. If Freddie starts on 1, jumps to the right and takes hops of size 2, what
Jump, Frog, Jump 1 2 Freddie, the frog, loves to jump! Today he has decided to put numbers on the lily pads in the pond and do a lot of jumping. 1. If Freddie starts on zero, jumps to the right and takes
Section 6.4 Permutations and Combinations: Part 1
Section 6.4 Permutations and Combinations: Part 1 Permutations 1. How many ways can you arrange three people in a line? 2. Five people are waiting to take a picture. How many ways can you arrange three
COUNTING METHODS. Methods Used for Counting
Ch. 8 COUNTING METHODS From our preliminary work in probability, we often found ourselves wondering how many different scenarios there were in a given situation. In the beginning of that chapter, we merely
PERMUTATIONS AND COMBINATIONS
PERMUTATIONS AND COMBINATIONS 1. Fundamental Counting Principle Assignment: Workbook: pg. 375 378 #1-14 2. Permutations and Factorial Notation Assignment: Workbook pg. 382-384 #1-13, pg. 526 of text #22
Board Question 1. There are 5 Competitors in 100m final. How many ways can gold silver and bronze be awarded? May 27, / 28
Board Question 1 There are 5 Competitors in 100m final. How many ways can gold silver and bronze be awarded? Photograph of Usain Bolt running a race removed due to copyright restrictions. May 27, 2014
Math 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
The factorial of a number (n!) is the product of all of the integers from that number down to 1.
ointers 5.5 Factorial The factorial of a number (n!) is the product of all of the integers from that number down to 1. 6! 6 x 5 x 4 x 3 x 2 x 1 20 You should have a built-in button or function on your
Redwood High School. Department of Mathematics Advanced Algebra Test S2 #6.
Redwood High School. Department of Mathematics Advanced Algebra 2015-2016 Test S2 #6. Hard Worker's name: Find the indicated probability. 1) Of the 69 people who answered "yes" to a question, 12 were male.
Grade 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
THE ALGEBRA III MIDTERM EXAM REVIEW Name. This review MUST be turned in when you take the midterm exam
THE ALGEBRA III MIDTERM EXAM REVIEW Name This review MUST be turned in when you take the midterm exam ALG III Midterm Review Solve and graph on a number line. 1. x 6 14. 3x 1 5x 14 3. 4(x 1) (4x 3) Find
Nwheatleyschaller s The Next Step...Conditional Probability
CK-12 FOUNDATION Nwheatleyschaller s The Next Step...Conditional Probability Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) Meery To access a customizable version of
Let 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.
THOMAS WHITHAM SIXTH FORM
THOMAS WHITHAM SIXTH FORM Handling Data Levels 6 8 S. J. Cooper Probability Tree diagrams & Sample spaces Statistical Graphs Scatter diagrams Mean, Mode & Median Year 9 B U R N L E Y C A M P U S, B U R
MIND ACTION SERIES THE COUNTING PRINCIPLE AND PROBABILITY GRADE
MIND ACTION SERIES THE COUNTING PRINCIPLE AND PROBABILITY GRADE 12 MARK PHILLIPS THE COUNTING PRINCIPLE AND PROBABILITY GRADE 12 1. The basic product rule of choices: a1 a2 a3... an 2. The product rule
Organized Counting 4.1
4.1 Organized Counting The techniques and mathematical logic for counting possible arrangements or outcomes are useful for a wide variety of applications. A computer programmer writing software for a game
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}?
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
Maths Weekly Plan Year 1/2 Teacher: D. Orr Autumn 1 week 2: Number & Place Value w/c
M Write numbers to 100 in figures and words. I will call out a series of numbers and the children have to write the number on their whiteboard. Challenge children to write in words as well as numbers.
probability success failure sample space random variable probability distribution
probability success failure sample space random variable probability distribution Probability with Combinations Roman has a collection of 26 books 16 are fiction and 10 are nonfiction. He randomly chooses
Name: Class: Date: 6. An event occurs, on average, every 6 out of 17 times during a simulation. The experimental probability of this event is 11
Class: Date: Sample Mastery # Multiple Choice Identify the choice that best completes the statement or answers the question.. One repetition of an experiment is known as a(n) random variable expected value
Counting Methods. Mathematics 3201
Mathematics 3201 Unit 2 2.1 - COUNTING PRINCIPLES Goal: Determine the Fundamental Counting Principle and use it to solve problems. Example 1: Hannah plays on her school soccer team. The soccer uniform
Jessica 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,
Permutations 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
NEL 5.3 Probabilities Using Counting Methods 313
5.3 Probabilities Using Counting Methods GOAL Solve probability problems that involve counting techniques. INVESTIGATE the Math As a volunteer activity, 10 students want to put on a talent show at a retirement
Probability. 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
Fundamental Counting Principle 2.1 Page 66 [And = *, Or = +]
![Fundamental Counting Principle 2.1 Page 66 [And = *, Or = +]](/thumbs/90/102632904.jpg "Fundamental 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
Georgia Department of Education Common Core Georgia Performance Standards Framework CCGPS Analytic Geometry Unit 7 PRE-ASSESSMENT
PRE-ASSESSMENT Name of Assessment Task: Compound Probability 1. State a definition for each of the following types of probability: A. Independent B. Dependent C. Conditional D. Mutually Exclusive E. Overlapping
Introduction. Firstly however we must look at the Fundamental Principle of Counting (sometimes referred to as the multiplication rule) which states:
Worksheet 4.11 Counting Section 1 Introduction When looking at situations involving counting it is often not practical to count things individually. Instead techniques have been developed to help us count
Math 1101 Combinations Handout #17
Math 1101 Combinations Handout #17 1. Compute the following: (a) C(8, 4) (b) C(17, 3) (c) C(20, 5) 2. In the lottery game Megabucks, it used to be that a person chose 6 out of 36 numbers. The order of
7.4 Permutations and Combinations
7.4 Permutations and Combinations The multiplication principle discussed in the preceding section can be used to develop two additional counting devices that are extremely useful in more complicated counting
Test 4 Sample Questions
Test 4 Sample Questions Solve the problem by applying the Fundamental Counting Principle with two groups of items. 1) An apartment complex offers apartments with four different options, designated by A
Math Week in Review #4
Math 166 Fall 2008 c Heather Ramsey and Joe Kahlig Page 1 Section 2.1 - Multiplication Principle and Permutations Math 166 - Week in Review #4 If you wish to accomplish a big goal that requires intermediate
50 Counting Questions
50 Counting Questions Prob-Stats (Math 3350) Fall 2012 Formulas and Notation Permutations: P (n, k) = n!, the number of ordered ways to permute n objects into (n k)! k bins. Combinations: ( ) n k = n!,
Counting Methods and Probability
CHAPTER Counting Methods and Probability Many good basketball players can make 90% of their free throws. However, the likelihood of a player making several free throws in a row will be less than 90%. You
Section The Multiplication Principle and Permutations
Section 2.1 - The Multiplication Principle and Permutations Example 1: A yogurt shop has 4 flavors (chocolate, vanilla, strawberry, and blueberry) and three sizes (small, medium, and large). How many different
Probability 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
pre-hs Probability Based on the table, which bill has an experimental probability of next? A) $10 B) $15 C) $1 D) $20
1. Peter picks one bill at a time from a bag and replaces it. He repeats this process 100 times and records the results in the table. Based on the table, which bill has an experimental probability of next?
Probability, Permutations, & Combinations LESSON 11.1
Probability, Permutations, & Combinations LESSON 11.1 Objective Define probability Use the counting principle Know the difference between combination and permutation Find probability Probability PROBABILITY:
Determine the number of permutations of n objects taken r at a time, where 0 # r # n. Holly Adams Bill Mathews Peter Prevc
4.3 Permutations When All Objects Are Distinguishable YOU WILL NEED calculator standard deck of playing cards EXPLORE How many three-letter permutations can you make with the letters in the word MATH?
Lesson1.notebook July 07, 2013
Lesson1.notebook July 07, 2013 Topic: Counting Principles Today's Learning goal: I can use tree diagrams, Fundamental counting principle and indirect methods to determine the number of outcomes. Tree Diagram
Name: Exam I. February 5, 2015
Department of Mathematics University of Notre Dame Math 10120 Finite Math Spring 201 Name: Instructors: Garbett & Migliore Exam I February, 201 This exam is in two parts on 10 pages and contains 1 problems
Name: Practice Exam I. September 14, 2017
Department of Mathematics University of Notre Dame Math 10120 Finite Math Fall 2017 Name: Instructors: Basit & Migliore Practice Exam I September 14, 2017 This exam is in two parts on 10 pages and contains
Name: Permutations / Combinations March 17, 2014
1. A pizza establishment offers 12 kinds of meat topping (pepperoni, sausage, etc.) and 5 kinds of vegetable toppings (onions, peppers, etc). How many different two topping pizzas can be made using a combination
This unit will help you work out probability and use experimental probability and frequency trees. Key points
Get started Probability This unit will help you work out probability and use experimental probability and frequency trees. AO Fluency check There are 0 marbles in a bag. 9 of the marbles are red, 7 are
Fundamental. 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
Using a table: regular fine micro. red. green. The number of pens possible is the number of cells in the table: 3 2.
Counting Methods: Example: A pen has tip options of regular tip, fine tip, or micro tip, and it has ink color options of red ink or green ink. How many different pens are possible? Using a table: regular
Examples: 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
Alg 2/Trig Honors Qtr 3 Review
Alg 2/Trig Honors Qtr 3 Review Chapter 5 Exponents and Logs 1) Graph: a. y 3x b. y log3 x c. y log2(x 2) d. y 2x 1 3 2) Solve each equation. Find a common base!! a) 52n 1 625 b) 42x 8x 1 c) 27x 9x 6 3)
Ÿ 8.1 The Multiplication Principle; Permutations
Ÿ 8.1 The Multiplication Principle; Permutations The Multiplication Principle Example 1. Suppose the city council needs to hold a town hall meeting. The options for scheduling the meeting are either Monday,
Fundamental Counting Principle 2.1 Page 66 [And = *, Or = +]
![Fundamental Counting Principle 2.1 Page 66 [And = *, Or = +]](/thumbs/80/80865142.jpg "Fundamental 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.
1. An office building contains 27 floors and has 37 offices on each floor. How many offices are in the building?
1. An office building contains 27 floors and has 37 offices on each floor. How many offices are in the building? 2. A particular brand of shirt comes in 12 colors, has a male version and a female version,