Re: Binomial Coefficient Problem
- From: Jack Tomsky <jtomsky@xxxxxxxxxxxxx>
- Date: Tue, 31 Jan 2006 14:16:47 EST
> I have the following problem:
>
> I solved the probability of some event to be equal
> to:
> C(10,2)*C(k-10,18)/C(k,20).
>
> The problem asks to find the value of k for which
> that probability is
> maximized.
>
> So, I set C(10,2)*C(k-10,18)/C(k,20) = 1.
>
> Can somebody help me solve this problem? I think
> that some rule of
> binomial coefficients must apply to make this really
> simple, but can't
> think of which one. The answer is k=100, but I have
> no idea what
> procedure to follow to get it.
>
> Much thanks in advance.
>
Your probability acan be rewritten as proportional to
[(k-20)(k-21)...(k-27)]/[k(k-1)...(k-9)] or
[(k-20)/k}][(k-21)/(k-1)]...[(k-27)/(k-7)]/[(k-8)(k-9)].
I ran these calculations on Excel for a wide range of k and found it to be maximized at k = 99 and 100.
Jack
.
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