Maximizing product of binomial coefficients

alexgalexg@yahoo.com · science forum beginner Joined: 08 Feb 2006 Posts: 2

Hi All,

I am looking for a reference to this problem:

Given n > m and k, such that both n and m are divisible by k. Maximize
the product:
$\binom{n1, m1} * \binom{n2, m2} * ... * \binom{nk, mk}$
where $\binom{n, m}$ denotes binomial coefficient

subject to constraints
$n1 + n2 + \ldots + nk = n$ and
$m1 + m2 + \ldots + mk = m$

The answer seems to be $\binom{n/k, m/k} ^ k$
I would appreciate any reference to a place (book, paper, etc ) where
this or similar problem is solved/dicussed?

Thanks,
Alex

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