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Is a generic solution possible to this problem
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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,

$0 \leq W \leq A$, $0 \leq R \leq B$, $0 \leq G \leq C$

I would like to know if there is any other reference for this though.

by Active (1.8k points)
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yes, generating function is one of the possible generic solution.

Similar examples are in this ref