Permutations and Combinations

An arrangement of objects in which the order is not important is called a combination.

This is different from permutation where the order matters.

For example, suppose we are arranging the letters A, B and C.

In a permutation, the arrangement ABC and ACB are different.

But, in a combination, the arrangements ABC and ACB are the same because the order is not important.

In how many ways can a coach choose three swimmers from among five swimmers?

There are 5 swimmers to be taken 3 at a time.

The coach can choose the swimmers in 10 ways.

There are 6 players to be taken 2 at a time.

They will need to play 15 games.