Permutation & Combination Calculator

How many ways to pick r things from n — with or without caring about order.

Result

Permutations: P(n, r)

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Combinations: C(n, r)

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n!

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r!

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(n − r)!

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The difference

Permutation — order matters. "How many ways to arrange 3 books on a shelf from 10 available?" → P(10,3) = 720.
Combination — order doesn't matter. "How many ways to choose 3 books to read (no specific order)?" → C(10,3) = 120.

Formulas

P(n, r) = n! / (n − r)!

C(n, r) = n! / (r! · (n − r)!)

Quick sanity check

C(52, 5) = 2,598,960 — the number of distinct 5-card poker hands. P(52, 5) = 311,875,200 — the same hands, counting each ordering.