\[\sum_{j,k} (-1)^{j+k}\binom{j+k}{k+l}\binom{r}{j}\binom{n}{k}\binom{s+n-j-k}{m-j}
\]
\[\begin{aligned}
0+1+2+3&=r \\
4+5+6+7&=n \\
8+9&= s-r \\
0+1&=j \\
4+5&=k \\
1+5&=k+l \\
0+1+3+7+9&=m \\
x&=(-1)^{0+1+4+5}
\end{aligned}
\]
\[\begin{aligned}
0+1+2+3&=r \\
4+5+6+7&=n \\
8+9&= s-r \\
1-4&=l \\
0+1+3+7+9&=m \\
x&=(-1)^{l+0+5}
\end{aligned}
\]
\[\begin{aligned}
1+2&=r \\
4+7&=n \\
8+9&= s-r \\
1-4&=l \\
2+4+8&=n-m+s \\
x&=(-1)^{l}
\end{aligned}
\]
\[\begin{aligned}
1+2&=r \\
4+7&=n \\
2+4&=r-l \\
8&=n-m+s-r+l \\
9&= m-n-l \\
x&=(-1)^{l}
\end{aligned}
\]
\[Ans=(-1)^l \binom{n+r}{n+l}\binom{s-r}{m-n-l}
\]