\[\sum_{j,k} (-1)^{j+k}\binom{j+k}{k+l}\binom{r}{j}\binom{n}{k}\binom{s+n-j-k}{m-j} \]\[\begin{aligned} 0+1+2+3&=r \\ 4+5+6+7&=n \\ 8+9&= s-r \\ 0+1&=j \\ 4+5&=k \\ 1+5&=k+l \\ 0+1+3+7+9&=m \\ x&=(-1)^{0+1+4+5} \end{aligned} \]\[\begin{aligned} 0+1+2+3&=r \\ 4+5+6+7&=n \\ 8+9&= s-r \\ 1-4&=l \\ 0+1+3+7+9&=m \\ x&=(-1)^{l+0+5} \end{aligned} \]\[\begin{aligned} 1+2&=r \\ 4+7&=n \\ 8+9&= s-r \\ 1-4&=l \\ 2+4+8&=n-m+s \\ x&=(-1)^{l} \end{aligned} \]\[\begin{aligned} 1+2&=r \\ 4+7&=n \\ 2+4&=r-l \\ 8&=n-m+s-r+l \\ 9&= m-n-l \\ x&=(-1)^{l} \end{aligned} \]\[Ans=(-1)^l \binom{n+r}{n+l}\binom{s-r}{m-n-l} \] 标签：begin,end,具体,5.83,数学,binom,aligned From： https://www.cnblogs.com/alfalfa-w/p/17261954.html