2C0

2C0 is a binomial coefficient, written as “2 choose 0” and read as two choose zero. It represents the number of ways to select zero elements from a set of two elements, which is exactly one way: the empty subset. Therefore 2C0 equals 1. In standard notation this is nCk or C(n,k), with n = 2 and k = 0 in this case.

A general property is that for any nonnegative integer n, nC0 = 1. More broadly, the binomial coefficient nCk is defined for integers with 0 ≤ k ≤ n; if k < 0 or k > n, the value is considered 0 in combinatorial contexts.

The value also appears in the binomial theorem. The expansion (x + y)^n = sum_{k=0}^n nCk x^{n−k} y^k uses nC0 as the first term of the expansion, which is always 1 when x precedes y. In Pascal’s triangle, the first and last entries of each row are 1, corresponding to nC0 and nCn.

Generalizations extend the concept to non-integer and complex numbers using the generalized binomial coefficient, which still yields 1 for k = 0. Thus 2C0 = 1 is consistent with both the integer and generalized definitions. For completeness, 2C1 = 2 and 2C2 = 1, while 2Ck = 0 for k > 2 in standard combinatorial interpretation. See also binomial coefficient and Pascal’s triangle.