← All Calculators

Combinatorics Calculator — Free Online Calculator

Calculates permutations and combinations for counting problems.

What is it?

The combinatorics calculator computes permutations (ordered arrangements) and combinations (unordered selections) from n items taken r at a time.

Formula

Permutations: P(n,r) = n! / (n−r)! Combinations: C(n,r) = n! / (r! × (n−r)!) With repetition allowed: Permutations: n^r Combinations: C(n+r−1, r)

Example

Choose 3 from 7: C(7,3) = 7! / (3! × 4!) = 5040 / (6 × 24) = 35 ways. Arrange 3 from 7: P(7,3) = 7!/4! = 210 ordered sequences.

Loading calculator…