Combinations & Permutations

Instantly calculate exactly how many ways you can select items from a set. Supports astronomically large outputs.

Total Set Size (n)

Amount to Choose (r)

Does Order Matter?

Replacement Allowed?

Combinations (nCr)

n! / [r! (n - r)!]

Total Number of Ways

2,598,960

What's the difference?

The easiest way to remember the difference is: Permutation = Position.

Combinations (Order does NOT matter): Think of a poker hand or making a fruit salad. If you have a hand of 5 cards, it doesn't matter what order you were dealt them in; your hand is the same. (Apples, Bananas, Grapes is the same salad as Grapes, Apples, Bananas).
Permutations (Order DOES matter): Think of a padlock combination or a race. If the winning sequence is Horse A, Horse B, Horse C, you don't win the bet if they cross the line as C, B, A. Order is strictly enforced.
Replacement: If replacement is allowed, it means you can pick the same item multiple times (like a slot machine spinning a "7" on three different reels). If replacement is not allowed, once you pick an item, it is removed from the pool (like dealing from a deck of cards).