Calculate the total number of ways to arrange n objects in a circle.

Enter the total number (n) and the number of selected items (r) and click the "Calculate circular permutations" button to calculate and display the total number of ways to arrange n different items in a circle.

It also shows how to calculate the total number of arrangements.

Please enter a positive integer up to 10,000 for Number to arrange.

A permutation is a sequence of several distinct things arranged in a row.

A circular permutation is a sequence in which your choices are arranged in a circular fashion.In the case of circular permutations, any number that is the same when rotated is counted as one.

For example, let's say you arrange the three letters A, B, and C in a circle.

In the case of permutations, there are six ways to arrange the numbers, but in the case of circular permutations, there is only one way if the numbers are the same when rotated, so ABC, BCA, and CAB also count as one way.

In this case, there are two ways to arrange the numbers: "ABC" and "ACB".

When calculating the total number of ways to arrange pieces using circular permutations, there is only one way that something can be rotated to be the same, so we will fix one location and consider it.

By fixing one location, we can calculate the total number by considering the rest as permutations without considering rotations.

For example, let's say you arrange the four letters A, B, C, and D in a circle.

If we fix the top number as A, we are left with three permutations.

Therefore, the total number of arrangements is 3! = 3×2, or 6.

In this way, the total number of ways to arrange the numbers in a circular permutation is the total number of numbers (n) minus 1.

So the formula for circular permutation is: