Combinatorics

Combinatorics is the study of counting.

Introductory combinatorics

The two most basic and fundamental ideas are that of permutations and combinations. In essence, the permutation is the number of ways to create a subset of a larger set if order matters (i.e. A, B, C is different from A, C, B). Similarly, the combination is the number of ways to create a subset of a larger set if order does NOT matter (i.e. A, B, C is the same as A, C, B).

Intermediate combinatorics

An important result of counting techniques is the formulation of the Principle of Inclusion-Exclusion (PIE).