Combinations & Permutations Calculator

Count the ways to choose or arrange r items from a set of n (nCr and nPr).

Result

Combinations (nCr)

120

Permutations (nPr)

720

How it works

nPr = n!/(n−r)!, nCr = nPr ÷ r!

Permutations count arrangements where order matters; combinations count selections where it does not. Choosing 3 from 10 gives 120 combinations and 720 permutations.

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Frequently asked questions

What is the difference?

Permutations care about order (1-2-3 ≠ 3-2-1); combinations do not.

When do I use combinations?

When you only choose a group — lottery numbers, teams, committees — and order is irrelevant.

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