Key Concepts: Permutations and Combinations

Permutation

An arrangement of objects where order matters.

P(n, r) = n! / (n − r)!

Combination

A selection of objects where order does not matter.

C(n, r) = n! / [r!(n − r)!]

When to Use Which

• Use permutations for arrangements, rankings, sequences, passwords.
• Use combinations for groups, committees, selections.

Special Cases

• 0! = 1
• P(n, n) = n!
• C(n, 0) = C(n, n) = 1