GlenCalc

Permutation and combination calculator

How many ways can you choose r things from n? It depends on whether order matters and whether the same item can be chosen twice.

Your answer

Combinations nCr (order doesn’t matter)120
Permutations nPr (order matters)720
Combinations with repetition220
Permutations with repetition (nʳ)1,000

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How we worked it out

Updated as you change the numbers.

  1. nPr = n! ÷ (n − r)!. nCr = n! ÷ (r! (n − r)!). With repetition: nʳ ordered, C(n + r − 1, r) unordered.

Method and assumptions

Permutations count ordered arrangements; combinations count selections where order doesn’t matter, so nCr = nPr ÷ r!. Results are exact, using whole-number arithmetic of any size.

Questions

How many ways to choose 3 from 10?

120 combinations, or 720 ordered permutations.

Sources

Method and figures checked on . Every worked answer on this page is covered by an automated test. Found a mistake? Tell us.

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