Permutation & Combination Calculator
Calculate nPr (permutations) and nCr (combinations) with step-by-step formulas.
| Type | Formula | Expanded | |
|---|---|---|---|
| P(10,3) | n! / (n-r)! | 10! / (10-3)! = 10! / 7! | |
| C(10,3) | n! / ((n-r)! x r!) | 10! / (7! x 3!) = nPr / 3! |
Permutations (order matters)
720
Combinations (order ignored)
120
Permutations vs. combinations
A permutation counts arrangements where order matters: P(n,r) = n! / (n-r)!. A combination counts selections where order does not matter: C(n,r) = n! / ((n-r)! x r!). For C(n,r), this calculator uses the multiplicative formula to avoid large intermediate values and stay within JavaScript number precision.
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