Permutation and Combination Videos

In this permutation and combination tutorial we will lern how to find the number of possible arrangements in a set of objects. Let's start by watching the following two videos.

Definition - Permutations

An arrangement of a set of objects in a certain order is called a PERMUTATION. To find the number of permutations of a certain set, use the factorial notation.

Example 1

Kerri wants an ice cream cone with one scoop of chocolate, one scoop of vanilla, and one scoop of strawberry. In how many ways can the scoops be arranged on the cone?

Long Solution

The following SIX arrangements are possible:

(chocolate, vanilla, strawberry)
(chocolate, strawberry, vanilla)
(vanilla, chocolate, strawberry)
(vanilla, strawberry, chocolate,)
(strawberry, chocolate, vanilla)
(strawberry, vanilla, chocolate)

Quick Solution

To quickly find the number of arrangements, use the factorial notation:

3! = 3 x 2 x 1 = 6 arrangements

Example 2

In how many ways can you arrange 5 books on a bookshelf?


5! = 5 x 4 x 3 x 2 x 1 = 120 ways

Example 3

Tom rented six movies. In how many different ways can he watch the six videos?


6! = 6 x 5 x 4 x 3 x 2 x 1 = 720 ways

Example 4

The password of a computer program is made-up of 4 different digits. How many different passwords can exist?


4! = 4 x 3 x 2 x 1 = 24 passwords

Definition - Combinations

A COMBINATION is a selection of items in which the order of the elements is not considered.

Example 5

Return from this Permutation and Combination Tutorial to Probability Videos.