A binomial coefficient, often denoted as n choose k or C(n, k), represents the number of ways to choose k elements from a set of n distinct elements without regard to the order of selection. It is calculated using the formula 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 algebra. They appear in the expansion of binomial expressions, as described by the Binomial Theorem, which states that (x + y)^n can be expanded into a sum involving binomial coefficients.