Combinatorics is used to count or enumerate combinations and permutations, crucial for solving problems involving probability and selection.

Combinatorics is a branch of mathematics focused on counting, arranging, and combining objects. In competitive programming, combinatorics is essential for solving problems that involve permutations (arrangements) and combinations (selections) of elements. It plays a crucial role in problems related to probability, optimization, or enumeration, where you need to count how many ways something can happen. For example, problems involving binomial coefficients, Pascal’s triangle, or the inclusion-exclusion principle often rely on combinatorics. Mastering basic combinatorics and knowing how to efficiently compute large factorials or binomial coefficients modulo a prime can give you a significant advantage in many competitive programming problems.