Permutation: Circular

How to solve a circular permutation: formula, 1 example, and its solution.

Formula

Formula

The number of ways
to arrange n things in a circle is
(n - 1)!.

This is the circular permutation formula.

Example

Example

Solution

There are 5 students.
They are sitting at a round table.

This is arranging 5 students
in a circle.

So the number of the ways is,
5 - 1,
4!.

4! = 4⋅3⋅2⋅1

Factorial

4⋅3 = 12
2⋅1 = 2

12⋅2 = 24

So the answer is 24.