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I've been looking at hypergeometric probability problems and came across this equation. Can someone explain to me why $\sum_{j=0}^{n-1}\frac{\binom{M-1}{j}\binom{(N-1)-(M-1)}{(n-1)-j}}{\binom{N-1}{n-1}}=1$? Take into consideration that I am using $N, M, n$ as parameters where there are $N$ total objects with $M$ "special" or unique objects, and $n$ is a selection sample.

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    johhny and @Graphth, would you care to take a look at [this answer/question](http://meta.math.stackexchange.com/a/3809/7850)?2012-03-13

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