basic

Combinations (nCr) Calculator

C(n,r) = n! / (r! · (n−r)!).

Compute the number of combinations C(n, r) — the number of ways to choose r items from n items without regard to order: C(n, r) = n! / (r!(n−r)!). Also known as the binomial coefficient "n choose r". Use for probability, combinatorics, and statistical sampling.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

C(n,r) = n! / (r!(n−r)!).

In depth

Compute the number of combinations C(n, r) — the number of ways to choose r items from n items without regard to order: C(n, r) = n! / (r!(n−r)!). Also known as the binomial coefficient "n choose r". Use for probability, combinatorics, and statistical sampling.