Statistics 9 min read

Combinations vs Permutations: Formulas, Differences & Examples

Learn the difference between combinations (order does not matter) and permutations (order matters). Master nCr and nPr counting formulas.

Table of Contents

Combinations vs Permutations Key Difference

The core distinction in counting theory comes down to one question: Does the order of arrangement matter?

Permutations (Order Matters)

Use permutations when sequence matters (e.g. lock combinations, race winners, seating arrangements).

Formula
ⁿPᵣ = n! ÷ (n − r)!

Combinations (Order Does Not Matter)

Use combinations when choosing a subset without regard to order (e.g. choosing lottery numbers, selecting a team of 3 from 10 people).

Formula
ⁿCᵣ = n! ÷ [r! × (n − r)!]
Σ
Reviewed by Applied Math Specialists • Editorial Policy
Updated: August 11, 2026

Related Interactive Calculators

Practice Tools