# What is Combination?

In this section we look at a method of selecting subsets of a larger set in which order is not counted. We shall call such subsets combinations of n elements taken r at a time. As an illustration, let us list all the combinations of 5 elements taken 2 at a time. Let the set of 5 elements be {1, 2, 3, 4, 5}. The list of combinations are

{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}

{2, 4}, {2, 5}, {3, 4}, {3, 5}, {4, 5}

The next result gives us the number of combinations of n distinct things taken r at a time.