  Drisko \cite{drisko} proved (essentially) that every family of $2n-1$
matchings of size $n$ in a bipartite graph possesses a partial rainbow matching
of size $n$. In \cite{bgs} this was generalized as follows: Any $\lfloor
\frac{k+2}{k+1} n \rfloor -(k+1)$ matchings of size $n$ in a bipartite graph
have a rainbow matching of size $n-k$. We extend this latter result to
matchings of not necessarily equal cardinalities.
  Settling a conjecture of Drisko, we characterize those families of $2n-2$
matchings of size $n$ in a bipartite graph that do not possess a rainbow
matching of size $n$. Combining this with an idea of Alon \cite{alon}, we
re-prove a characterization of the extreme case in a well-known theorem of
Erd\H{o}s-Ginzburg-Ziv in additive number theory.
