Here we are interested in knowing number of solutions to the following integral equation problem:
$W + R + G = K$, where W, R, G represent number of white, red and green balls respectively, such that,
$0 \leq W \leq A$, $0 \leq R \leq B$, $0 \leq G \leq C$
Please refer this article (after example 3) for the general formula
I would like to know if there is any other reference for this though.