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Combination is defined as $C(n,k) = n! / k!(n-k)!$, where n & k are non-negative integers.

Now, the definition can be extend to C(r,k), where r is real number and k is an integer:

C(r,k) = r(r-1)...(r-k+1)/k! , where k>=0;        = 1 , where k = 0;        = 0 , where k < 0. 

Question: is it possible to extend the definition even further, to be based on 2 real numbers, C(r,s), where both r and s are real numbers?

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    Take a look at [Beta function](http://en.wikipedia.org/wiki/Beta_function).2012-08-30
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    Possible duplicate of http://math.stackexchange.com/questions/188596/what-is-the-usage-of-combination-cr-k-where-r-extends-to-real-number In particular, Fly by Night's answer, and Tunococ's comment about the beta function provide an answer to this question.2012-08-30
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    I should note that extending definitions without a particular purpose in mind is maybe an amusing sport, but rather pointless in itself. And some day somebody might have a serious application that requires a _different_ extension.2012-08-30

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