Fundamental Concept: Utilizes algebraic techniques to understand combinatorial identities.
Definition: If S is a set with n elements, then there are ( \binom{n}{k} ) ways to select k distinct elements. These counts are referred to as binomial coefficients.
Binomial Expression and Theorem
Weak Definition
A binomial expression is the sum of two terms, which may include numbers or products of variables (e.g., 5, t, t^4).
The Binomial Theorem
Statement: For variables x, y and a natural number n: