# Number of ways of choosing K balls from A White,B Red and C Green Balls.

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Is a generic solution possible to this problem

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.

0
yes, generating function is one of the possible generic solution.

Similar examples are in this ref

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An urn contains 30 red balls and 70 green balls. What is the probability of getting exactly k red balls in a sample of size 20 if the sampling is done with replacement (repetition allowed)? Assume 0≤k≤20.
1 vote
The number of ways in which $2n$ white and $2n$ black balls can be arranged such that no consecutive $n$ white balls are together, is ${}^{2n+1}C_2 + {}^{4n}C_{2n}$ ${}^{2n+1}C_2 - {}^{2n+1}C_1. {}^{3n}C_{n} (-1)^n + {}^{4n}C_{2n}$ ${}^{2n+1}C_2+ (-1)^n. {}^{2n+1}C_1 . {}^{3n}C_n + {}^{4n}C_{2n}$ ${}^{2n+1}C_2+ (-1)^n. {}^{3n}C_n . {}^{2n+1}C_1$