Skip to Main Content
It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.

**Permutations **

A **Permutation** of a set is an ordered combination of its elements. The number of permutations of elements taken at a time is denoted by and is determined by:

##### the factorial notation is defined as:

**Example: **A physics olympiad team consists of 4 members. a) In how many ways can all members be arranged in a row for a photo? b) How many ways can the captain and vice-captain be chosen?

##### a) We can use either the fundamental counting principle or permutations to solve this problem. Let's use the fundamental counting principle:

##### This is a permutation problem in which we have 4 members and we take 4 at a time, therefore:

##### In the above equation we used:

##### b) This is a permutation problem in which we have 4 members and we take 2 at a time:

#####

**Example: **In how many ways can 5 girls and 4 boys be seated on a bench? a) If there are no restrictions. b) If girls and boys alternate.

##### a) If there are no restrictions, we have:

##### b) If boys and girls alternate, we should have a girl on each end:

##### This permutation problem can be interpreted as having 5 girls and taking 5 at a time and having 4 boys and taking 4 at a time: