This combination calculator calculates the number of all possible combinations that can result by taking a subset of items from a larger given set of items.

Combinations of (n):*
Taken (r) at a time:*

What is a combination?

In mathematics, a combination refers to a way of selecting items from a larger set of items called collection, while the order of selection does not matter. Usually when speaking about this concept people use the expression: combination of n things taken k at a time where repetitions are not allowed.

The algorithm of this combination calculator uses the formula explained below:

C(n;r) = n!/(r!(n - r)!)


C = total number of combinations available;

n= the number of possibilities / the number of distinct objects;

r = the sample elements / taken “r” at a time.

Example of a combination result

Assuming we have 20 elements in total while we try to figure out which is the total number of possible combinations if the elements are taken as 10 each time?

Answer: 184756.

10 Apr, 2015