How it works
A permutation is an arrangement where order matters. Picking a president, vice president and treasurer from 10 people gives 10 × 9 × 8 = 720 permutations, because the same three people in different roles count as different outcomes.
Without repetition, each item can be used once, so the count is n! ÷ (n − r)!. With repetition, every position can be any of the n items, giving nʳ, as with a 4-digit PIN (10⁴ = 10,000).
If order does not matter, use combinations instead. The number of permutations is always at least as large as the number of combinations.
Formula
nPr = n! ÷ (n − r)! · With repetition: nʳ
Questions people ask
What is the difference between a permutation and a combination?
Permutations count ordered arrangements; combinations count unordered groups. ABC and CBA are two permutations but the same combination.
How many ways can I arrange all n items?
Set r equal to n. The answer is n!, so 5 books can be arranged on a shelf in 5! = 120 ways.
What does 0! equal?
0! is defined as 1, so nPn = n! ÷ 0! = n!, and nP0 = 1 (there is exactly one way to choose nothing).