1. Algebra II 10.1: Apply the Counting Principle and Permutations

2. Fundamental Counting Principle

3. Application of Fundamental Counting Principle Ex. 1) You have 3 shirts, 4 pairs of pants, and 2 pairs of shoes. How many outfits of 1 shirt, 1 pair of pants, and 1 pair of shoes can you create? Ex. 1) You have 3 shirts, 4 pairs of pants, and 2 pairs of shoes. How many outfits of 1 shirt, 1 pair of pants, and 1 pair of shoes can you create?

4. Application of Fundamental Counting Principle Ex. 2a) How many different license plates are possible if you have 3 letter followed by 3 digits if digits can repeat? Ex. 2a) How many different license plates are possible if you have 3 letter followed by 3 digits if digits can repeat? 2b)How many plates are possible if letters and digits cannot repeat? 2b)How many plates are possible if letters and digits cannot repeat?

5. Factorial ! n! = n·(n-1)·(n-2)·(n-3)·(n-4)·…1 n! = n·(n-1)·(n-2)·(n-3)·(n-4)·…1 7!= 7·6·5·4·3·2·1 7!= 7·6·5·4·3·2·1 7! = ____ 7! = ____

6. Factorial Expand and simplify Expand and simplify 1.) 2.) 3.) 4.)

7. Permutations An ordering of n objects where order is important is a permutation of the objects. An ordering of n objects where order is important is a permutation of the objects. The number of permutations of n objects is n!. The number of permutations of n objects is n!. Ex. 1a) 10 people are in a race. How many different ways can the people finish in the race? Ex. 1a) 10 people are in a race. How many different ways can the people finish in the race?

8. Permutations The # of permutations = where The # of permutations = where n = total # of objects, r = # you are taking. n = total # of objects, r = # you are taking. Ex. 1b.) 10 people are in a race. How many different ways can 3 people win 1 st, 2 nd, and 3 rd place? Ex. 1b.) 10 people are in a race. How many different ways can 3 people win 1 st, 2 nd, and 3 rd place?

9. Ex. 2 Find the number of permutations

10. Permutations with Repetition The number of permutations of n objects where an object repeats s # of times. The number of permutations of n objects where an object repeats s # of times.

11. Find the number of distinguishable permutations of the letters in the word. 1.) MATH 2.) TALLAHASSEE 3.) CLASSROOM

12. ASSIGNMENT

13. Find the number of distinguishable permutations of the letters in the word. 4.) ABERDEEN 5.) CLASSROOM 6.) MATH

14. Permutations Ex. 2.) You are burning a CD with 13 songs. How many ways can the songs be arranged on the CD? Ex. 2.) You are burning a CD with 13 songs. How many ways can the songs be arranged on the CD?

15. Permutations Ex. 3.) Ms. Wynes’s 2 nd period class is playing 7up with a total of 19 students in the class. How many different ways can the people be chosen if order is important? Ex. 3.) Ms. Wynes’s 2 nd period class is playing 7up with a total of 19 students in the class. How many different ways can the people be chosen if order is important?