If we expand the expression

$\displaystyle (x_1+x_2+x_3+x_4)^6$

what will be the largest coefficient that occurs?

My attempt:

My hunch is that the coefficient should belong to one of the middle terms.

$\displaystyle \dbinom{6}{2,2,1,1}=\frac{6!}{2!2!1!1!}=180$

Is it right? I'm not sure how to prove it, though.