I wanted to prove following equation
$\binom{x+y+n-1}{n} = \sum\_{k=0}^{n} \binom{x+n-k-1}{n-k} \binom{y+k-1}{k}$

Using Vandermonde's identity 
$\binom{a+b}{t} = \sum\_{k=0}^{t} \binom{a}{t-k} \binom{b}{k}$

whereas $a=x+n-k-1$ and $b=y+k-1$ but it doesn't add up. 

Where is my mistake? How do i proof it?