What is the difference between a permutation and a combination?

Combinations ignore order (which items you pick), permutations count order too. They are related by P(n,r) = C(n,r) × r!.

How is C(n,r) computed?

C(n,r) = n! / (r! × (n-r)!), evaluated as a running product with cancellation so intermediate values never blow up.

Up to 1000 for combinations and permutations and 2000 for factorials, all computed exactly.

It is 1 by definition, which keeps identities such as C(n,0)=1 consistent.

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🎯Combination and Permutation Calculator - C(n,r), P(n,r) and n!

Compute C(n,r), P(n,r) and n! without running out of digits: results are exact big integers, shown in full alongside scientific notation, with combinations with repetition and the total number of subsets included.

Free · No sign-up · Runs in your browserLast updated: 2026-10-26

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How to use Combinations

1Choose combinations, permutations or factorial
2Enter n and r
3Read the exact value, or copy the scientific-notation form for very long results

FAQ

What is the difference between a permutation and a combination?: Combinations ignore order (which items you pick), permutations count order too. They are related by P(n,r) = C(n,r) × r!.
How is C(n,r) computed?: C(n,r) = n! / (r! × (n-r)!), evaluated as a running product with cancellation so intermediate values never blow up.
How large can n be?: Up to 1000 for combinations and permutations and 2000 for factorials, all computed exactly.
What is 0! ?: It is 1 by definition, which keeps identities such as C(n,0)=1 consistent.