The Binomial Coefficient is a mathematical concept that represents the number of ways to choose a subset of items from a larger set, without regard to the order of selection. It is denoted as n choose k or C(n, k), where n is the total number of items and k is the number of items to choose. The formula for calculating it is C(n, k) = n! / (k! * (n-k)!), where "!" denotes factorial, the product of all positive integers up to that number. Binomial coefficients are commonly used in combinatorics, probability, and statistics. They appear in the expansion of binomial expressions, as described by the Binomial Theorem. For example, the coefficients in the expansion of (a + b)ⁿ are the binomial coefficients C(n, k) for k = 0 to n. This makes them essential for solving problems related to combinations and distributions.