How can I transform the following sum s.t. one can apply the Vandermonde convolution and thus obtain a solution for this summation?
$$ \sum_{k \leq n} \binom{n-k} r \binom m {k-s} (-1)^k,\quad \text{integers } n, r, s\ge 0 $$
I thought about this a bit but don't even get how we can pull the $(-1)^k$ into the binomial coefficient or how to swap the arguments of the first coefficient.