Combinations & Permutations Calculator
Enter the total number of items (n) and the number chosen (r) to find the number of combinations and permutations.
How combinations and permutations differ
Permutations (nPr) count the number of ways to arrange r items chosen from n, where order matters — picking A then B is different from picking B then A. It's calculated as nPr = n! / (n−r)!.
Combinations (nCr) count the number of ways to choose r items from n where order doesn't matter — picking A and B is the same as picking B and A. It's calculated as nCr = nPr / r!, since each combination corresponds to r! different orderings counted separately in nPr.
Frequently asked questions
When should I use combinations instead of permutations?
Use combinations when the order of selection doesn't matter (like choosing a committee of 3 people from 10), and permutations when it does (like awarding 1st, 2nd, and 3rd place from 10 competitors).
Why is nCr always smaller than or equal to nPr?
Because nCr = nPr / r!, and r! is 1 or greater, nCr can never exceed nPr — they're equal only when r is 0 or 1, since 0! and 1! both equal 1.
What does nC0 or nCn equal?
Both always equal 1 — there's exactly one way to choose zero items (choose nothing) or to choose all n items (choose everything).