13.2 – Find Probabilities Using Permutations A permutation is an arrangement of objects in which order is important. For instance, the 6 possible permutations.

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Presentation transcript:

13.2 – Find Probabilities Using Permutations A permutation is an arrangement of objects in which order is important. For instance, the 6 possible permutations of the letters A, B, and C are shown. ABC ACB BAC BCA CAB CBA

13.2 – Find Probabilities Using Permutations Example 1: Consider the number of permutations of the letters in the word JULY. a.In how many ways can you arrange all of the letters. b.In how many ways can you arrange 2 of the letters?

13.2 – Find Probabilities Using Permutations Example 1b: Consider the number of permutations of the letters in the word BRIGHTEN. a.In how many ways can you arrange all of the letters. b.In how many ways can you arrange 2 of the letters?

13.2 – Find Probabilities Using Permutations Factorial: In Example 1, you evaluated the expression 4x3x2x1. This expression can be written as 4! and is read “4 factorial.” For any positive integer n, the product of the integers from 1 to n is called n factorial and is written as n!. The value of 0! is defined to be 1. n! = n x (n – 1) x (n – 2) x ….x 3 x 2 x 1

13.2 – Find Probabilities Using Permutations

Example 2: You band has written 12 songs and plans to record 9 of them for a CD. In how many ways can you arrange the songs on the CD?

13.2 – Find Probabilities Using Permutations Example 2b: You have 14 CDs. You can arrange 12 of the 14 in a CD wallet. In how many ways can you arrange the CDs in the CD wallet?

13.2 – Find Probabilities Using Permutations Example 3: For a town parade, you will ride on a float with your soccer team. There are 12 floats in the parade, and their order is chosen at random. Find the probability that your float is first and the float with the school chorus is second.