Overview
Combinatorics is the study of counting, in particular, counting the number of ways that a set of items can be chosen or arranged.
Combinatorics has a close connection to statistics because it is useful in enumerating all the different possibilities that a given situation could take. As a simple example, given a deck of cards, combinatorics could help determine that number of possible different hands of five cards there are, and how many of those represent a straight.
Equal Probability Assumption
The typical assumption when using combinatorics is that each possibility is equally likely. If this is assumed, the probability of any event is then just the number of possible occurrences of that event, divided by the total number of possible events.