Aim: What is a permutation? Do Now: Evaluate n(n -1)(n-2)(n-3). 1. n = 52. n = 10.

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Presentation transcript:

Aim: What is a permutation? Do Now: Evaluate n(n -1)(n-2)(n-3). 1. n = 52. n = 10

Vocabulary Permutation – an arrangement or listing in which order is important Factorial – the product of all counting numbers beginning with the number given (n) and counting backward to 1 Example 6! = 6 × 5 × 4 × 3 × 2 × 1

Finding a permutation An ice cream shop has 31 flavors. Carlos wants to buy a 3-scoop sundae. How many different arrangements can he make if order is important? ______ × ______ × ______ # of possible flavors for the first scoop # of possible flavors for the second scoop # of possible flavors for the third scoop

Using Permutation Notation An ice cream shop has 31 flavors. Carlos wants to buy a 3-scoop sundae. How many different arrangements can he make if order is important? P(31, 3) = 31 × 30 × 29 or 31 P 3 = 31 × 30 × 29

Factorials A factorial is a specific type of permutation in which an arrangement is made from all members of the set 4! = P(4,4) = 4 × 3 × 2 × 1 OR 4! = 4 P 4 = 4 × 3 × 2 × 1

Practice Evaluate. 1.P(5,2) 2.8P4 3.How many possibilities can you arrange all letters in the word math. 4.If six people are running a race, how many different arrangements can there be to award a 1 st, 2 nd, and 3 rd place prize?