Permutation Calculator

Calculate the number of permutations nPr — ordered selections of r items from n — with or without repetition.

What is the Permutation Calculator?

A permutation is an arrangement where order matters, such as podium finishes or PIN codes.

How does it work?

Without repetition, nPr = n! ÷ (n − r)!. With repetition, each of the r positions can be any of n items, giving nʳ.

Formula

nPr = n! ÷ (n − r)!
With repetition: nʳ

Example

Gold, silver and bronze among 10 runners: 10P3 = 720. A 4-digit PIN: 10⁴ = 10,000.

Frequently asked questions

Permutation or combination?

If swapping the order gives a different outcome, use permutations; otherwise use combinations.

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