Permutations and combinations

Combinations and permutations deal with the various ways that we can select objects from a set to make various subsets in which order may or may not matter. For permutations, order matters, and for combinations, order does not matter.

One way to think of this is using phone numbers. Imagine that we know that the phone number of someone we want to call includes a combination of numbers: 1, 2, 3, 4, 5, 6, 7, 8 , 9 and 0. If we weren't trying to call someone specific, we could pick any combination of the 10 numbers, and we could try calling that number. The order wouldn't matter and we could choose any 10 numbers in any order we wanted. This would constitute a combination.

A permutation on the other hand, requires that the numbers be in a specific order. If the phone number of the friend we're trying to call is 324-156-9087, we need to dial the number in exactly that order. If we don't, we'll call someone else, or no one at all. In both cases, we're using the same 10 digits, but in the first case, we're not concerned with who we reach, while in the second case we are.

Explore the rest of this section to learn more about combinations and permutations, particularly with respect to how they are used in probability.