1. PERMUTATIONS

2. Permutation Method of counting when order matters
Example: Coming in first, second, or third
Combination locks

3. Examples How many ways can 5 students be arranged in 5 desks?
There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

4. Examples How many ways can 5 students be arranged in 5 desks?
There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

5. Examples How many ways can 5 students be arranged in 5 desks?
There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

6. Examples How many ways can 5 students be arranged in 5 desks?
There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

7. Examples How many ways can 5 students be arranged in 5 desks?
There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

8. Examples How many ways can 5 students be arranged in 5 desks?
There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

9. Examples How many ways can 5 students be arranged in 5 desks?
There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

10. Examples How many ways can 5 students be arranged in 5 desks?
There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

11. Examples
How many ways can 7 runners finish a race?

12. Examples
How many ways can 7 runners finish a race?

13. Examples
How many ways can 7 runners finish a race?

14. Permutation Notation n = Number of “objects” to choose from
r = Number of “objects” in the arrangement

15. Simplify

16. Simplify

17. Simplify

18. Simplify

19. Simplify

20. Simplify

21. Simplify

22. Simplify

23. Simplify

24. Example
How many permutations are there for the letters H , O , M , E , S

25. Example
How many permutations are there for the letters H , O , M , E , S

26. Example
How many permutations are there for the letters H , O , M , E , S

27. Example
How many permutations are there for the letters H , O , M , E , S

28. Examples
20 students volunteer to be on a 3-person committee. How many different permutations are there?

29. Examples
20 students volunteer to be on a 3-person committee. How many different permutations are there?

30. Examples
20 students volunteer to be on a 3-person committee. How many different permutations are there?

31. Examples
20 students volunteer to be on a 3-person committee. How many different permutations are there?

32. ASSIGNMENT
12.6: 1 – 8, 20 – 22, 24,