nCk is the number of k-element subsets of n-elements. The quantites nCk are called *binomial coefficients* because of their role in the Binomial Theorem.

- recall the binomial theorem states (x + y)^n can be expanded as the sum of terms
`a * x^b * y^c`

, where a is the binomial coefficient nCb

Important identity: `nCk = nC(n-k)`

. Choosing a k-element subset B from an n-element set uniquely identifies the complement A \ B of B in A, which is an (n-k)-subset of A.