The Gaussian Coefficient, often denoted as n \choose k, represents the number of ways to choose k elements from a set of n elements, where the order of selection does not matter. It is calculated using the formula n \choose k = \fracn!k!(n-k)!, where ! denotes factorial, the product of all positive integers up to that number. These coefficients are significant in combinatorics and are closely related to the binomial theorem. They appear in the expansion of (x + y)^n, where the coefficients of the terms correspond to the Gaussian Coefficients.