Summation Proof with Binomial Theorem

Prove the following statement:

$$$\sum\limits_{r + s = t} {\left( { - 1} \right)^r \left( \begin{array}{c} n + r - 1 \\ r \\ \end{array} \right)} \left( \begin{array}{c} m \\ s \\ \end{array} \right) = \left( \begin{array}{c} m - n \\ t \\ \end{array} \right)$$$

Any initial help is appreciated.

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 Mentor Well, what have you done? What is the definition of, say, m choose s?