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9 4 Permutations

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9 4 Permutations

1. 1. 9-4 Permutations p 381 Find the number of permutations of a set of objects
2. 2. Work the hands on mini lab on page 381 with a partner
3. 3. We want to choose president and vice president from 4 people. <ul><li>Demonstrate with volunteers. </li></ul><ul><li>Use the fundamental counting principle to find number of outcomes. </li></ul>
4. 4. A permutation is an arrangement, or listing, of objects in which order is important . <ul><li>President and vice president vs committee members </li></ul>
5. 5. Example from mini lab
6. 6. Factorial (n!) <ul><li>5!=5*4*3*2*1=120 </li></ul>
7. 7. Find each of the following <ul><li>7! </li></ul><ul><li>3! </li></ul><ul><li>2!(3!) </li></ul>
8. 8. Ex) in how many ways can the starting six players of a volleyball team stand in a row for a picture? <ul><li>Turn and talk---why is this a permutation? </li></ul>
9. 9. Ex) The finals of the Middle School Appalachian League features 8 swimmers. In how many ways can the swimmers finish in first of second place? <ul><li>Why is this permutation? </li></ul>
10. 10. Ex) A team of bowlers has five members who bowl one at a time. In how many orders can they bowl? <ul><li>Why is this permutation? </li></ul>
11. 11. A school fair holds a raffle with 1 st , 2 nd , and 3 rd prizes. Seven people enter the raffle. How many ways can the three prizes be awarded?
12. 12. In how many ways can you arrange four books on a shelf.
13. 13. In how many ways can you award 1 st and 2 nd prize form a group of 6?
14. 14. In how many ways can 7 people line up at a ticket window?
15. 15. In how many ways can you arrange the letters in the word eighty?
16. 16. In how many ways can you choose a leading man and an understudy from 11 actors?
17. 17. Coach Malone has an 8-member volleyball team. He told his team that he would start six different players every game. How many games would it take to do this? <ul><li>Why is this not permutation? </li></ul>
18. 18. The International Club is selling hot dogs at eh Spring Carnival. Customers can select three toppings from among chili, onions, cheese, mustard, or relish. <ul><li>Is this permutation? </li></ul>
19. 19. What are some key words that help you know it is a permutation?
20. 20. What are some key words that show it is not a permutation?
21. 21. Handout—left side only LINE CODES <ul><li>With a partner </li></ul>
22. 22. Journal <ul><li>How do you find a permutation? </li></ul>
23. 23. n P r n objects chosen r at a time <ul><li>A school fair holds a raffle with 1 st , 2 nd , and 3 rd prizes. Seven people enter the raffle. How many ways can the three prizes be awarded? </li></ul><ul><li>7 P 3 </li></ul>graphing calculator
24. 24. p 382: 3-19, 21, 22, 23