Permutation & Combination Calculator

Calculate permutations, combinations, and factorial values with step-by-step solutions

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Permutation: P(n,r) = n!/(n-r)!
Order matters

Combination: C(n,r) = n!/(r!(n-r)!)
Order doesn't matter

Factorial: n! = n × (n-1) × ... × 1
Product of all positive integers ≤ n

Circular Permutation: (n-1)!
Arrangements in a circle

Permutation with Repetition: n^r
r items from n with repetition

Combination with Repetition: C(n+r-1,r)
r items from n with repetition

Permutation: Arrangements where order matters
Example: ABC ≠ BAC

Combination: Selections where order doesn't matter
Example: {A,B,C} = {B,A,C}

Factorial: Product of descending integers
Example: 5! = 5×4×3×2×1 = 120