Permutation & Combination Calculator

Calculate permutations and combinations. Essential for probability, statistics, and counting problems.

n (Total Items)

r (Selected Items)

Calculation Type

Tab to move between fields

Result

720

FormulaP(10,3) = 10! / (10-3)!

How to Use This Calculator

Enter n (the total number of items) and r (the number being selected or arranged).
Choose Permutation to count ordered arrangements: P(n,r) = n! / (n−r)! — order matters.
Choose Combination to count unordered selections: C(n,r) = n! / (r!(n−r)!) — order does not matter.
r must be ≤ n and both must be non-negative integers; C(n,r) = C(n, n−r) by symmetry.
Permutations are used for rankings and sequences; combinations are used for lottery odds and team selection.
For very large n, results may exceed safe integer limits and be expressed in scientific notation.

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Formula

Permutation: P(n,r) = n!/(n-r)!, Combination: C(n,r) = n!/(r!(n-r)!)

Calculate probability of single events, combined events (AND/OR), permutations, and combinations.

Calculate factorial (n!) and double factorial (n!!). Useful for permutations, combinations, and mathematical calculations.

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