Permutations

Definition of Permutation

An arrangement of a collection of things in which the order of selection matters.

Ex: You have to visit Andrew’s house (A), Betty’s house (B), and Carlos’ house (C) but you have not decided the order. What are the different ways you can visit all 3 houses.

A,B,C

A,C,B

B,A,C

B,C,A

C,A,B

C,B,AEach arrangement is one permutation of the elements A, B, and C. In

other words, there are 9 total permutations.

Permutation v Non-Permutation

Which problem(s) below represents a permutation problem? Explain why and why not.

Craig needs to select an ATM pin. He can choose any 4 digit number using the integers 0 to 9.

The Lifetime TV Network has a total of 147 annual viewers. They are offering a promotion for the first three callers. The first caller wins $25, the second $15, and the third $1.

Joanne has 20 friends and needs to select 3 of them to go on vacation with her.

Repeats Allowed

Order does not Matter

How to Calculate the Total Number of Permutations

The total number of ways (without repeats) to choose AND arrange r objects from a set of n objects (order matters).

Ex: If there are 10 people in a race, how many different ways can the top 3 finishers be arranged?

10!7!

10!10 3 ! 10 9 8

!

!n r

nP

n r

72010 3P