12. Distribute $n$ identical (i.e., indistinguishable) footballs to $r$ football teams, so that each team gets at least $s_{1}$ footballs, but no more than $s_{2}\left(r s_{1} \leqslant n \leqslant r s_{2}\right)$ footballs. How many different ways are there to do this?
12. $\sum_{k=0}^{r}(-1)^{k}\binom{r}{k}\binom{n+r-s_{1} r-\left(s_{2}-s_{1}+1\right) k-1}{r-1}$.