Combination Calculator

Calculate the number of combinations nCr — ways to choose r items from n when order does not matter.

What is the Combination Calculator?

A combination is a selection where order is irrelevant, such as choosing a team or lottery numbers.

How does it work?

nCr = n! ÷ (r! × (n − r)!). With repetition allowed, it becomes (n + r − 1)Cr.

Formula

nCr = n! ÷ (r!(n − r)!)

Example

A 5-card hand from 52 cards: 52C5 = 25,98,960 combinations.

Frequently asked questions

Why is nCr always smaller than nPr?

Each combination of r items can be ordered in r! ways, so nPr = nCr × r!.

Related tools

Enable JavaScript to use this calculator.