Binomial Coefficient Problem

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.

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