Summation Proof with Binomial Theorem

[ChaoticLlama]

Prove the following statement:

\[<br /> \sum\limits_{r + s = t} {\left( { - 1} \right)^r \left( \begin{array}{c}<br /> n + r - 1 \\ <br /> r \\ <br /> \end{array} \right)} \left( \begin{array}{c}<br /> m \\ <br /> s \\ <br /> \end{array} \right) = \left( \begin{array}{c}<br /> m - n \\ <br /> t \\ <br /> \end{array} \right)<br /> \]<br />

Any initial help is appreciated.

 

[cristo]

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