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Archiver > GENEALOGY-DNA > 2002-07 > 1026220647

From:
Subject: [DNA] re: Poisson vs. others
Date: Tue, 9 Jul 2002 08:17:27 -0500 (CDT)

> From: John F. Chandler <>

> Gregg wrote:
> > I don't know any other way. In my case, I can calculate 432! on other
> > computers which are readily available to me. Nevertheless, I would be
> > interested to learn how to determine exact binomial without having to
> > determine the (n) factorial.

> The point is that the binomial coefficient "N take M" is N!/M!/(N-M)!,
> and that expression is all you need. You don't need the individual
> factors. Therefore, if you find yourself in the regime where M is close
> to N, you note that N!/M! = Nx(N-1)x(N-2)x...x(M+1). What's more, you
> can do the whole thing in purely integer arithmetic by alternating:
> N x (N-1) / 2 x (N-2) / 3 x ... x (M+1) / (N-M). (This is because of
> a theorem that shows successively that Nx(N-1) is always divisible
> exactly by 2, and Nx(N-1)x(N-2) is always divisible exactly by 2x3,
> and so on.)

It should also be pointed out that factorials of large numbers can be
readily found by using Sterling's approximation, or you can find the
logarithm of the factorial by simply adding the logarithms of all the
smaller positive integers.

432! = 4.272460 X 10^952

Also, it is generally an accumulation of binomial terms that is desired
and this can be approximated by a normal (Gaussian) distribution. This is
not an ad hoc approximation but rather a mathematically justified
numerical approximation.

Steve

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