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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