Algebra II 10.1: Apply the Counting Principle and Permutations Fundamental Counting Principle 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? 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? 2b)How many plates are possible if letters and digits cannot repeat? Factorial ! n! = n·(n-1)·(n-2)·(n-3)·(n-4)·…1 7!= 7·6·5·4·3·2·1 7! = ____ Factorial Expand and simplify 1.) 2.) 3.) 4.) An Permutations ordering of n objects where order is important is a permutation of the objects. 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? Permutations The # of permutations = where n = total # of objects, r = # you are taking. Ex. 1b.) 10 people are in a race. How many different ways can 3 people win 1st, 2nd, and 3rd place? Ex. 2 Find the number of permutations Permutations with Repetition number of permutations of n objects where an object repeats s # of times. The Find the number of distinguishable permutations of the letters in the word. 1.) MATH 2.) TALLAHASSEE 3.) CLASSROOM ASSIGNMENT Find the number of distinguishable permutations of the letters in the word. 4.) ABERDEEN 5.) CLASSROOM 6.) MATH Permutations Ex. 2.) You are burning a CD with 13 songs. How many ways can the songs be arranged on the CD? Permutations Ex. 3.) Ms. Wynes’s 2nd 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?