Permutation Formula

The permutation formula calculates the number of ordered arrangements that can be made from a group of objects. It is used when the order of selected items matters, such as arranging people in positions or choosing ranked outcomes.

Permutation Formula

nPr = n! ÷ (n − r)!

Here, n is the total number of available items, r is the number of items selected, and ! represents factorial.

Understanding Factorials

A factorial is the product of all positive integers from a number down to 1. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are used in the permutation formula to count possible ordered arrangements.

Example

If 5 students are available and 2 positions must be filled in order, the number of arrangements is 5P2 = 5! ÷ 3! = 20.

When to Use Permutations

Use permutations when changing the order creates a different outcome. If order does not matter, a combination formula is usually more appropriate.