Welcome! Worksheet Counting Principal, Permutations, Combinations. Updates: U4T is 12/12

Transcription

1 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 is not in SB; all homework's will be a worksheet.

2 1 Counting Principal 2 Permutations 3 Combinations 4 Cool-Down! Agenda

3 Setting up your Notebook Leave one page blank for supplemental notes. Today s Lesson #: ---- Topic: Fundamental Counting Principle, Combination, Permutation LO#1: Solve word problems involving the fundamental counting principle, permutations, and combinations.

4 Fundamental Counting Principal You are at a carnival. One of the carnival games asks you to pick a door and then pick a curtain behind the door. There are 3 doors and 4 curtains behind each door. Create a tree diagram on your whiteboard that represents this situation. How many curtains can you choose from?

5 Fundamental Counting Principal Practice: (1) There are 3 trails leading to Camp A from your starting position. There are 3 trails from Camp A to Camp B. Use a tree diagram to represent the situation. How many trails lead to camp B?

6 Fundamental Counting Principal Table Talk: o Is there a relationship between the number of decisions to be made and the possible outcomes? Fundamental Counting Principle A method to identify the total number of ways different events can occur. The possible outcomes is the product of the decisions. Example: When there are m ways to do one thing, and n ways to do another, then there are m n ways of doing both.

7 Fundamental Counting Principal Now that you are familiar with the Fundamental Counting Principle attempt #2-5 in your groups. Be prepared to write your solution on the main whiteboard.

8 Permutations In your groups on one whiteboard identify all of the different rearrangements of the letters R A N. (It does not have to spell something real.) Record each word you create. In your groups on one whiteboard identify all of the different rearrangements of the letters R A N S. (It does not have to spell something real.) Record each word you create. o Is there a relationship to the order and the number of different letters I give you?

9 Permutations Permutations All possible arrangements of a collection of items where the order is important. ORDER MATTERS! Let n be the number of items: n (n-1) (n-2) (n-3) (1) This is called factorial! Factorial The product of the natural numbers less than or equal to the number. Let n be the number of items: n (n-1) (n-2) (n-3) (1) Example: 6! = = 720

10 Permutations

11 Permutations Sometimes you may not want to order an entire set of items. Suppose that I wanted to call on three of you only. So, I only want 3 out of (say we had a smaller class for the sake of this example) 8 students. How many possibilities for students can I have?

12 Permutations We will do #9, then you will complete #10-11 in your groups. (9) The ski club with ten members is to choose three officers captain, co-captain & secretary, how many ways can those offices be filled? (10) Suppose you are asked to list, in order of preference, the three best movies you have seen this year. If you saw 15 movies during the year, in how many ways can the four best be chosen and ranked? (11) In a production of Grease, eight actors are considered for the male roles of Danny, Kenickie, and Marty. In how many ways can the director cast the male roles?

13 Combinations Lastly, we will also discuss Combinations; picking items in a group where order does not matter. In English we use the word combination loosely, without thinking if the order of things is important. My fruit salad is a combination of apples, grapes, and bananas. The combination to the safe was 472. o Discuss which sentence represents order and which represents without order.

14 Combinations If the order does not matter, it is a Combination. If the order does matter, it is a Permutation. Combination A grouping of items in which order does not matter. There are generally fewer ways to select items when order does not matter. Example: There are 6 ways to order 3 items, but they are all the same combination. 6 permutations {ABC, ACB, BAC, BCA, CAB, CBA} 1 combination {ABC}

15 Combinations Combinations

16 Whiteboards! A team of 17 softball players needs to choose three players to reiill the water cooler. How many ways could these players be selected?

17 Combinations Practice with Combinations: (12) Katie is going to adopt kittens from a litter of 11. How many ways can she choose a group of 3 kittens? (13) A teacher wants to send 4 students to the library each day. There are 21 students in the class. How many ways can he choose 4 students to go to the library on the first day?

18 Click MATH Go right to PRB Permutation is 2:nPr Combination is 3:nCr Factorial is 4:! Calculator!

19 Cool-Down! On your whiteboard we will do the following practice: practice_quizzes/alg2/alg2_pq_prs_01.html