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
Combinations
120
10! / (3! × 7!).
- n10
- r3
- C(n, r)120
- P(n, r)For comparison (ordered)720
- Ratio P/C= r!6
Step-by-step
- C(10, 3) = n! / (r!(n−r)!) = 10! / (3! × 7!).
- Compute as product: ∏ᵢ₌₀^(3-1) (n−i)/(i+1) = 120.
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: order doesn't matter (subsets). Permutations: order matters (sequences). C(n,r) = P(n,r) / r!.
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