corresponding variables X_s. Now setting all of the X_s equal to the unlabeled variable X, so that the product becomes (1 + ''X'')^''n'', the term for each k-combination from S becomes X^k, so that the coefficient of that power in the result equals the number of such k-combinations.

Binomial coefficients can be computed explicitly in various ways. To get all of them for the expansions up to (1 + ''X'')^''n'', one can use (in addition to the basic cases already given) the recursion relation