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alexgalexg@yahoo.com
science forum beginner

Joined: 08 Feb 2006
Posts: 2

Posted: Thu Feb 09, 2006 12:30 am    Post subject: Maximizing product of binomial coefficients

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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