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Combinations & Permutations Calculator

Calculate combinations (nCr) and permutations (nPr). Find how many ways to choose or arrange items.

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Formula

C(n,r) = n! / (r!(n-r)!) — P(n,r) = n! / (n-r)!

Combinations vs Permutations

Combinations count how many ways to choose items when order doesn't matter. Picking 3 people for a team from 10 people: C(10,3) = 120 ways.

Permutations count how many ways to arrange items when order matters. Assigning 3 prizes to 10 people: P(10,3) = 720 ways.

Frequently Asked Questions

Combination vs permutation?

Combinations: order doesn't matter (choosing a team). Permutations: order matters (arranging in a line).

What does n! (factorial) mean?

n! = n × (n-1) × (n-2) × ... × 1. For example, 5! = 5×4×3×2×1 = 120.