Permutation Calculator

What are Permutations?

A permutation is an arrangement of objects where the order matters. P(n,r) represents the number of ways to arrange r objects from n total objects.

Formula

P(n,r) = n! / (n-r)!

Where: n ≥ r ≥ 0

Applications

• Arranging people in a line or seats
• Creating passwords with unique characters
• Race finishing positions
• Tournament brackets and rankings

Examples

P(5,3): Ways to arrange 3 people from 5 total

P(5,3) = 5!/(5-3)! = 120/2 = 60

P(4,4): Ways to arrange 4 people from 4 total

P(4,4) = 4!/0! = 24/1 = 24