Permutation and combination calculator

How many ways to arrange or choose r items from n, with or without repetition.

Questions people ask

What is the difference between a permutation and a combination?

Permutations count ordered arrangements; combinations count selections where order doesn’t matter. Picking a president and vice-president from 10 people is 90 permutations; picking any 2 people is 45 combinations.

What are the formulas?

nPr = n! ÷ (n − r)!, nCr = n! ÷ (r! (n − r)!). With repetition: nʳ arrangements and (n + r − 1)Cr selections.