Combinations Calculator C(n, r)

C(n, r) = n! / (r!(n−r)!). Number of ways to choose r items from n where order doesn't matter.

Result

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General calculation reads

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Scientific calculator (Casio fx-991EX)

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How to use this calculator

Enter n (total) and r (chosen).
Read combinations + comparison to permutations.

About this calculator

Combinations count selections where order doesn't matter. C(52, 5) = 2,598,960 (poker hands). C(n,r) = n! / (r!(n-r)!), but computing via product (n)(n-1)...(n-r+1) / r! avoids factorial overflow for moderately large n. Symmetric: C(n,r) = C(n, n-r). Used in probability, combinatorics, and statistics (binomial coefficient).

Frequently asked

Combinations vs. permutations?+

Combinations: order doesn't matter (subsets). Permutations: order matters (sequences). C(n,r) = P(n,r) / r!.

Pascal's triangle?+

Each entry is C(n, r). Row 5 col 2 = C(5,2) = 10. Triangle relates combinations recursively.

Why "n choose r"?+

Read the symbol C(n, r) or "n choose r" — both refer to the same count.

Real-world?+

Lottery odds: 6 from 49 → C(49,6) = 13,983,816 possible tickets. Card hands: C(52,5) = poker; C(52,2) = ~1326 starting hands in Texas Hold'em.

Symmetry?+

C(n, r) = C(n, n-r). Choosing r to include equals choosing n-r to exclude.

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