What is the difference between combinations and permutations?

Permutations count arrangements where order matters (ABC ≠ BAC). Combinations count selections where order doesn't matter (ABC = BAC = CAB). Lottery numbers are combinations; race placements are permutations.

What is the formula for combinations?

C(n,r) = n! / (r! × (n-r)!). For example, C(5,2) = 5! / (2! × 3!) = 10 — there are 10 ways to choose 2 items from 5.

Combinations and Permutations Calculator

Quick answer: Enter n (total items) and r (items chosen) to get both combinations C(n,r) and permutations P(n,r).

Calculate combinations (order doesn't matter) and permutations (order matters) from n items choosing r. Used in probability, statistics, and counting problems.

Last reviewed: April 2026Report an error

n (total items)

r (items chosen)

Combinations C(n,r)

120

C(10,3) = 120, P(10,3) = 720.

Combinations C(n,r)

120

Permutations P(n,r)

720

How to Use This Combinations & Permutations Calculator

1Enter n — the total number of items in your set.
2Enter r — how many items you want to choose or arrange.
3Read C(n,r) for combinations and P(n,r) for permutations.

Frequently Asked Questions

: Permutations count arrangements where order matters (ABC ≠ BAC). Combinations count selections where order doesn't matter (ABC = BAC = CAB). Lottery numbers are combinations; race placements are permutations.
: C(n,r) = n! / (r! × (n-r)!). For example, C(5,2) = 5! / (2! × 3!) = 10 — there are 10 ways to choose 2 items from 5.

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Combinations and Permutations Calculator

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