# Permutation (nPr) Calculator & Formula

LAST UPDATE: October 16th, 2020

## Definition – What are permutations?

Permutations are the number of different combinations of different orders that can be made from a group of items.
For example, the numbers 1, 2, and 3 have the following six different 2 number permutations:
1 2
1 3
2 1
2 3
3 1
3 3
The numbers 1, 2, 3, and 4 have the following 12 different 2 number permutations:
1 2
1 3
1 4
2 1
2 3
2 4
3 1
3 2
3 4
4 1
4 2
4 3
The numbers 1, 2, 3, and 4 have the following 24 different 3 number permutations:
1 2 3
1 2 4
1 3 2
1 3 4
1 4 2
1 4 3
2 1 3
2 1 4
2 3 1
2 3 4
2 4 1
2 4 3
3 1 2
3 1 4
3 2 1
3 2 4
3 4 1
3 4 2
4 1 2
4 1 3
4 2 1
4 2 3
4 3 1
4 3 2

## Formula – How are permutations calculated?

Permutations are calculated by the formula:

Number of Items! ÷ ((Number of Items – Items in Each Permutation)! x Items in Each Permutation!)

### Example

How many different permutations of 3 can be made from 10 different items?

Permutations = 10! ÷ ((10 – 3)! x 3!)

Permutations = 3628800 ÷ (7! x 3!)

Permutations = 3628800 ÷ (5040 x 6)

Permutations = 3628800 ÷ 30240

Permutations = 120