1. Permutations Course 3 Chapter 11-2

2. Permutation 1. A permutation is an arrangement of elements from a single set. 2. Repetitions are not allowed. 3 The order in which the elements are arranged is significant. A permutation is an ordered arrangement of objects.

3. Example 1 List all the two-digit numbers that are possible from using 1, 2, and 3. Are repetitions allowed?

4. Answer 11 21 31 12 22 32 13 23 33 Nine possible numbers

5. Fundamental Counting Principle 3 possible first digits X 3 possible second digit = 9 possible numbers

6. Example #2 Remember: A permutation in an ordered arrangement of objects. List all the ways it’s possible to elect a President and Vice-president from Dave, Jane, and Bob.

7. Answer President Vice –president Dave Jane Dave Bob Jane Dave Jane Bob Bob Jane Bob Dave 6 Possibilities

8. Example 3 How many possible ways can you line up 4 people selected from a class of 35? Does order matter in this problem?

9. Answer The first person can be selected in 35 ways. The next can be selected in 34 ways, the third can be selected in 33 ways, and the fourth can be selected in 32 ways. By the Fundamental Counting Principle the total number of permutations is: 35 x 34 x 33 x 32 = 1,256,640

10. Formula Can write the problem using notation 35P4 Meaning “Number of 35 objects chosen 4 at a time.” Write 35! But only use the first 4 numbers 35x34x33x32

11. Example 4 In how many different ways can you line up a half dollar, quarter, dime, nickel and penny.

12. Answer 120 Five choices (half dollar, quarter, dime, nickel and penny) 5! = 5 x 4 x 3 x 2 x 1

13. Example 6 A CD has 11 songs. Find in how many orders you can play the songs.

14. Answer 39,916,800 ways Solve using 11!

15. Example 6 Simplify 10P3 Number of 10 objects chosen at 2 at a time.

16. Formula n! / (n-r)! 10! / (10-2)! = 10 x 9