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My guess is that it is a sub-field of Discrete Math known as combinatorics but I cannot find it here.

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it's "discrete" math, not "discreet" math. They are two very different words. – Bean Oct 16 '11 at 19:14
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Note that the number $\binom{n}{k}$ "n choose k" is a Binomial coefficient and that you find on your Wikipedia link. – t.b. Nov 8 '11 at 0:20

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Such kind of problems appear in every subfield of combinatorics.

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And that's mainly because binomial coefficients are a basic and central concept in combinatorics... – Fernando Martin Oct 16 '11 at 19:07

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