Counting & Combinatorics: Intro

Counting and combinatorics are important areas of discrete mathematics that study ways to count and arrange objects.

We use counting principles to solve problems involving arrangements, selections, and groupings.

Combinatorics helps computer scientists analyze algorithms and understand data structures. In addition, as we'll see in the next Topic, counting is also the basis for computing useful probabilities of various events.

Counting and combinatorics also provide tools for analyzing advanced discrete structures like graphs.

Key ideas in counting include the Addition Principle, Multiplication Principle, permutations, and combinations.

More advanced ideas include the Binomial Coefficient, Inclusion-Exclusion Principle, and the Pigeonhole Principle.