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Permutations and Combinations EQ: What is a permutation? Vocabulary Sample Space: A list of all possibly outcomes Tree Diagram: A visual method for counting. The last column shows the same space Ex Example: Leah wants to make a sandwich. She has 2 types of bread, 3 cheeses, and 4 types of lunch meat. How many different sandwiches can she make? Create a tree diagram. Fundamental Counting Principle If an event M can occur m ways and is followed by N which can occur n ways, then the even M followed by N is equal to m‧n. Ex) If you own 3 shirts and 5 pants, you can create 15 outfits. Factorial (!) The expression n! (read n factorial) is the product of all positive integers beginning with n and counting backwards to 1. 5! = 5‧4‧3‧2‧1 Ex) How many ways can 4 books be arranged on a shelf? Permutation A arrangement (or listing) in which order is important. (example: lottery numbers, standing in line, arranging books on a shelf) n! n pr (n r )! n: number of objects r: how many you are using at a time Examples: 1) If there are 6 students, how many ways can you line up 4 of them? 2) How many ways can you arrange 4 out of 8 books on a shelf? Combination An arrangement where order is NOT important n! n Cr r!(n r )! n: number of objects r: how many you are using at a time Example: 3) How many combination of 3 letters from the set {a,b,c,d,e}are there? 4) Sue got to pick two prizes from a grab bag of 12 prizes. How many combinations of 2 prizes are possible? 5) How many combinations of 3 students can be made from a class of 20?