Combinatorics: solving for coefficient of x^n term

[Armbru35]

Hi, I'm currently taking a Discrete Mathematics class and cannot seem to work out this one problem, we need to find the x^10 term in order to determine its coefficient of the equation f(x)=(x+x^2+x^3+x^4+x^5+x^6)^3 I know the answer is to be 27 from a previous problem (we are to use this method to verify our answer) but I can't seem to figure it out. I started with thinking of trying to solve x^3/((1-x)^3)-the sum of x^n starting with n≥7, but that doesn't seem to be working. Any suggestions would be appreciated!

 

[awkward]

Hint:

$$f(x) = x^3 \left( \frac{1-x^6}{1-x} \right) ^ 3$$

 

[Armbru35]

Ahhh...I was confused for a second but I was doing the binomial theorem wrong. Thank you so much that helped tremendously!