1. Lesson 9-4 Pages 381-383 Permutations Lesson Check 9-3

2. What you will learn! How to find the number of permutations of a set of objects.

3. PermutationFactorial

4. What you really need to know! The expression n factorial (n!) is the product of all counting numbers beginning with n and counting backward to 1. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

6. What you really need to know! A permutation is an arrangement, or listing, of objects in which order is important. You can use the Fundamental Counting Principle to find the number of possible arrangements.

7. Link to Pre-Made Lesson

8. Example of a Permutation: You must pick 2 letters from the letters A, B, C to form a two letter code for computer access. Each letter can only be used once. How many codes can be made. 32 x = 6 AB AC BA BC CA CB

9. Example 1: Find the value of the expression. 4 x 3 x 2 x 1 24 4!

10. Example 2: Find the value of the expression. 3 x 2 x 1 x 5 x 4 x 3 x 2 x 1 720 3! 5!

11. Example 3: A team of bowlers has five members who bowl one at a time. In how many orders can they bowl?

12. Example 3: This is a permutation. There are 5 choices for the first bowler, 4 for the second, 3 for the third, 2 for the fourth, and 1 for the fifth. 120 Written as 5!

13. Example 4: A school fair holds a raffle with 1 st, 2 nd, and 3 rd place prizes. Seven people enter the raffle. How many ways can the three prizes be awarded?

14. Example 3: This is part of a permutation. There are 7 choices for 1 st place, 6 for 2 nd place, and 5 for 3 rd place. 210 Written as 7 x 6 x 5.

15. Page 382 Guided Practice #’s 3-6

17. Pages 381-382 with someone at home and study examples! Read:

18. Homework: Page 383 #’s 7-19 all #’s 21-24 Lesson Check 9-4

20. How many different three-digit security codes can be made from the digits 1, 2, 3, 4, and 5 if no digit is repeated in a code?

21. Page 585 Lesson 9-4

22. Lesson Check 9-4

23. Prepare for Mid-Test! Page 384 #’s 1-16

27. 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6

28. 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6

29. 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6

30. 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6

31. 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6

32. 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6