Find the number of permutations — ways to arrange r items from n when order matters. Enter n and r.
Usage Tip
Permutations are combinations times r factorial — multiply C(n,r) by the orderings of the chosen items.
Order matters
There are always more permutations than combinations for the same n and r.
The matching combination count is shown for comparison.
P(n, n) equals n factorial.
A permutation is an arrangement in which order matters, so picking A then B is different from picking B then A. The number of ways to arrange r items chosen from n is n factorial divided by n minus r factorial. Choosing three runners for first, second and third place out of ten gives 10 times 9 times 8, or 720 outcomes.
If order does not matter, you want combinations instead, which divide the result by r factorial. Factorials grow very quickly, so even modest values of n produce huge numbers. The number of items chosen, r, cannot be larger than the number available, n, unless repetition is allowed, which is a different calculation.