Combinatorial identities are mathematical equations that express relationships between different combinatorial quantities. They often involve counting the number of ways to arrange or select items from a set, using symbols like n, k, and C(n, k) to represent combinations. These identities help simplify complex counting problems and reveal underlying patterns in combinatorial structures. One well-known example of a combinatorial identity is the Binomial Theorem, which states that the expansion of (x + y)^n can be expressed as a sum of terms involving C(n, k). Such identities are essential in fields like probability, statistics, and computer science, where counting and arrangement play crucial roles.