CM CalcMentor Calculators that explain the answer.

Counting methods

Permutation and Combination Calculator

Calculate arrangements when order matters and selections when order does not matter.

Order changes the question

Use permutations for rankings, passwords and ordered arrangements. Use combinations for committees, lottery-style selections and unordered groups.

Example

With n = 10 and r = 3, permutations count ordered picks: 10 x 9 x 8 = 720. Combinations ignore order: 720 / 3! = 120.

Common mistakes

Ask whether ABC and CBA should count as different outcomes. If yes, use permutations. If no, use combinations.

Limitations

This calculator assumes selections without replacement. Problems with repeated choices, restrictions or probability weights need a different setup.

Last reviewed: 2026-05-17

Before relying on this result

Use this calculator together with the formula, assumptions, limitations and examples on the page. If the topic involves health, tax, lending, investment, legal, safety or current-rate decisions, treat the number as an estimate and check the relevant primary source or professional guidance.

Calculator metadata last reviewed: 2026-05-14.