Hi, I have the following problem that is solved, but I have no clue what formula the teacher uses to solve it... Thanks a lot for your help!

I have:

$\displaystyle (((1/6)*s)^{10})*((1-s^6)/(1-s))^{10}$

Which is equal to

$\displaystyle ((1/6)^{10})*(1-10s^6+...)*(1+10s+...)$

And the coefficient of $\displaystyle s^{27}$ (and the main thing I don't understand how the teacher gets it) is

$\displaystyle [(1/6)^{10}]*[(10C2)*(14C5)-(10C1)*(20C11)+(26C17)]$