When should I use combinations?
Use combinations when selecting the same items in another order does not create a different result.
Combinations and Permutations Calculator
Calculate nCr combinations and nPr permutations with exact integers.
Calculations happen locally. We do not send your values to our server.
Example
Choosing 2 items from 5 gives 10 combinations when order does not matter and 20 permutations when order matters.
Calculation method
Combinations use n!/(r!(n−r)!), calculated with integer cancellation. Permutations multiply n × (n−1) through r selected positions.
Important notes
Inputs must be whole numbers with 0≤r≤n≤1000. Very large answers are displayed as exact integers.
Frequently asked questions
When should I use permutations?
Use permutations when the order or assigned position of selected items matters.
What happens when r is zero?
There is exactly one way to select or arrange zero items, so both results equal one.