Combinations & Permutations

Calculate nCr combinations and nPr permutations with step-by-step factorial breakdowns.

n — total items

r — items chosen

Permutations P(n,r) — ORDER matters

P(n,r) = n! / (n−r)!

720

10 things taken 3 at a time (order matters)

Combinations C(n,r) — ORDER doesn't matter

C(n,r) = n! / (r! × (n−r)!)

120

10 things taken 3 at a time (order doesn't matter)

P(10,3) = C(10,3) × 3! → 720 = 120 × 6

When to use Permutations?

Use P(n,r) when order matters: arranging people in seats, creating PINs, ranking competitors, forming words from letters.

When to use Combinations?

Use C(n,r) when order doesn't matter: selecting a committee, choosing lottery numbers, picking a hand of cards, forming a team.

CombinationsPermutationsFactorialProbability

Calculate combinations C(n,r) and permutations P(n,r) for any n and r, with step-by-step factorial breakdowns and practical real-world examples.

Key Features

Combinations C(n,r)

Counts ways to choose r items from n when order does not matter: n! / (r!(n−r)!).

Permutations P(n,r)

Counts ways to arrange r items from n when order matters: n! / (n−r)!.

BigInt Precision

Uses JavaScript BigInt for exact integer results up to n = 170 — no floating-point rounding.

Step-by-Step

Shows all three factorials (n!, r!, (n−r)!) and the full calculation for n ≤ 20.

Formula Relationship

Displays the relationship P(n,r) = C(n,r) × r! for both values.

Quick Examples

One-click examples: poker hands, lottery, seating arrangements.