Find the number of combinations — ways to choose r items from n when order does not matter. Enter n and r.
Usage Tip
Choosing 3 from 10 is the same as leaving out 7 from 10 — that is why C(10,3) equals C(10,7).
Order does not matter
They are permutations divided by the number of orderings of each group.
The matching permutation count is shown for comparison.
C(n, r) equals C(n, n − r).
A combination counts the ways to choose r items from n when the order does not matter, so choosing A and B is the same as choosing B and A. The formula is n factorial divided by r factorial times n minus r factorial. Choosing a committee of three from ten people can be done in 120 ways.
Combinations are always smaller than the matching permutations, because each group of r items is counted once instead of in every possible order. The count is symmetric, so choosing r items to take is the same as choosing n minus r items to leave behind. Combinations are used in lotteries, card hands, and sampling problems.