(sorry, I really couldn't make a better title while still descriptive)
There is a box of $X$ red and $Y$ blue balls. There are $n$ labels, named $1,2, \ldots,n$.
We must put $x$ of those on red balls and $y$ of those on blue, where $x+y = n$.
In how many different ways can that be done.
We do distinguish between different balls of the same color.