Combinations & Permutations Calculator
Calculate combinations (nCr) and permutations (nPr) for any n and r. Learn factorial formulas and combinatorics.
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Frequently Asked Questions
Clear answers to common questions to help you use this calculator confidently.
What's the difference between combinations and permutations?
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What's the difference between combinations and permutations?
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Combinations: order doesn't matter (picking a team). Permutations: order matters (arranging a sequence). C(n,r) = n!/(r!(n−r)!), P(n,r) = n!/(n−r)!.
What is 10 choose 3?
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What is 10 choose 3?
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C(10,3) = 120. There are 120 ways to choose 3 items from 10 when order doesn't matter.
What happens if r is greater than n?
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What happens if r is greater than n?
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Both combinations and permutations are 0 — you can't choose or arrange more items than exist in the set. The calculator enforces n ≥ r.
Why is C(n,r) always equal to C(n, n−r)?
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Why is C(n,r) always equal to C(n, n−r)?
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Choosing r items to include is the same as choosing n−r items to leave out, so both selections describe the same set of outcomes. Example: C(10,3) = C(10,7) = 120.
Is there a limit on how large n can be?
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Is there a limit on how large n can be?
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This calculator supports n up to 170, since 171! exceeds the largest number JavaScript can represent precisely. For larger values, use logarithmic (log-factorial) methods instead.
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