Permutations and Combinations

Count permutations and combinations, with and without repetition.

Count arrangements

Total items n Chosen r

Permutations P(n, r): —

Combinations C(n, r): —

Permutations with repetition n^r: —

Combinations with repetition C(n + r - 1, r): —

P(n, r) = n! / (n - r)! and C(n, r) = n! / (r! (n - r)!).

Common questions about the free online permutations and combinations.

Enter the total number of items as n and how many you choose as r, then all four counts appear as you type.

Permutations count ordered selections, so ABC differs from CBA, while combinations count unordered groups where order does not matter.

It means an item can be chosen more than once, which multiplies the number of options and raises the counts considerably.

It means there are ten different ways to pick two items from five when order does not matter, such as AB, AC and AD.

For selections without repetition, no, because you cannot choose more items than you have. The tool reports zero in that case.

They appear in probability, card and lottery odds, password space estimates, scheduling and many counting problems.

Whole numbers are exact only up to about nine quadrillion, so bigger counts are shown in scientific notation instead.

No. All counting happens locally in your browser and no numbers you enter are sent anywhere.

Last updated: October 10, 2026