Maxima of discrete functions involving nPr, nCr, etc?

[cantgetaname]

Homework Statement

So I want to prove that the expression 20Cr×0.1^r 0.9^(20-r) reaches maximum value for r=(0.1)×20=2

Homework Equations

The Attempt at a Solution

I can prove it by trial and error but can't differentiate the expression because nCr isn't continuous.

 

[cantgetaname]

Found solution here:http://math.stackexchange.com/questions/855255/prove-maximum-term-in-the-expansion