1. Algebra II 10.1: Apply the Counting Principle and Permutations HW: HW: p.686-688 (6, 10, 14, 16, 26, 28, 34, 62-68 all) Quiz 10.1-10.3: Friday, 12/13

2. Fundamental Counting Principle If one event occurs m ways and another event occurs n ways, then both events occur ways. If one event occurs m ways and another event occurs n ways, then both events occur ways. (Can be applied for more than two events.) (Can be applied for more than two events.)

3. Application of Fundamental Counting Principle 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? 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 How many different license plates are possible if you have 1 letter followed by 2 digits followed by 3 letters if letters and digits can repeat? How many different license plates are possible if you have 1 letter followed by 2 digits followed by 3 letters if letters and digits can repeat? How many plates are possible if letters and digits cannot repeat? How many plates are possible if letters and digits cannot repeat?

5. Factorial What does 9! mean? What does 9! mean? Expand and simplify Expand and simplify 1.) 2.) 3.) 4.)

6. 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!. Example: Example: –10 people are in a race. How many different ways can the people finish in the race?

7. 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. Example: Example: –10 people are in a race. How many different ways can 3 people win 1 st, 2 nd, and 3 rd place?

8. Permutations You are burning a CD with 13 songs. How many ways can the songs be arranged on the CD? You are burning a CD with 13 songs. How many ways can the songs be arranged on the CD?

9. Permutations 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? 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?

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.) WYNES 2.) TALLAHASSEE 3.) MATAWAN

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