Permutations & Combinations
Permutations count arrangements where order matters; combinations count selections where it does not. This calculator finds nPr = n!/(n−r)!, nCr = n!/(r!(n−r)!) and the factorial n!, showing each step.
Frequently asked questions
What is the difference between a permutation and a combination?
A permutation counts ordered arrangements, so ABC and CBA are different; a combination ignores order, so they count once.
What does nCr mean?
nCr is the number of ways to choose r items from n without regard to order, equal to n!/(r!(n−r)!).
Can r be larger than n?
No. You cannot choose more items than are available, so r must be between 0 and n.