9C2

9C2, also written as C(9,2), is a binomial coefficient representing the number of ways to select 2 elements from a set of 9 elements without regard to order. It is computed as 9!/(2!(9−2)!) = (9×8)/2 = 36. Consequently, 9C2 equals 36. Due to the symmetry of binomial coefficients, 9C2 = 9C7.

This quantity appears in various counting problems involving unordered pairs from nine items, such as forming two-person teams from a group of nine people or selecting two lottery numbers from nine choices. In probability, if each pair is equally likely, there are 36 possible pairs. In mathematics, nCr forms the binomial coefficient family and appears in the expansion of (x+y)^n; it is listed in Pascal's triangle at row 9, column 2. Generalization: nCr is defined for integers n ≥ r ≥ 0 by nCr = n!/(r!(n−r)!).