# Maximum value of probability

This is my first post here. Apologies if there are any misformats or mis-tagging.

Also if the post doesn't belong here, sorry, and I will delete it.

I derived this formula from a probability calculation. How would I go about finding the maximum value for the following?

$\frac{T}{S}\frac{S!}{(S-D)!}\frac{(T-D)!}{T!}$

where

$T>S>D$

and T, S, and D are all integers.

Thank you.

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Hint: We can rewrite this as (by multiplying and dividing by $(D-1)!$) as $\frac{{S-1}\choose {D-1}}{{T-1}\choose {D-1}}$.