Combinatorics calculator

Counting methods

Permutation P(n,r): Order matters. P(n,r) = n!/(n−r)!. Arranging r items from n.

Combination C(n,r): Order doesn’t matter. C(n,r) = n!/(r!(n−r)!). Choosing r items from n.

Factorial

n! = n × (n−1) × ... × 2 × 1. 5! = 120. 0! = 1 (by convention).

When to use which

Arranging people in a line? Permutation. Choosing a committee? Combination. Selecting passwords? Permutation.