math calculators

Permutation Calculator

Calculate the number of ordered arrangements of r items from n

About this calculator

A permutation is an ordered arrangement. P(n,r) = n! / (n−r)! counts how many ways to arrange r items from n when order matters. Choosing a president, vice president, and secretary from 10 candidates: P(10,3) = 720. Order matters — ABC and BAC are different permutations.

How to use

P(5,2): arrangements of 2 from 5. 5!/3! = 5×4 = 20. If you rank gold, silver, bronze from 5 athletes, there are 20 possible outcomes.

Frequently asked questions

When does order matter (permutation vs combination)?

Order matters in permutations: a lock combination 1-2-3 differs from 3-2-1. Order does not matter in combinations: choosing a committee of 3 from 10 — the same 3 people form the same committee regardless of selection order.

What is P(n,n)?

P(n,n) = n! — the number of ways to arrange all n items. For 4 items: 4! = 24 arrangements.