The subset sum problem for finite abelian groups

Let G be a finite abelian group. A problem in combinatorics is to give an explicit formula for the number of subsets of G of size n which sum up to a given element of G. In this article we give a short proof, using character theory, of a formula for these numbers due to Li and Wan. We show that these numbers are nonzero except in four special cases. A similar formula is given when none of these subsets contain zero.