so I've searched a lot about this and I've seen a few solutions but I didn't understand any of them.
I have this equation which I'm meant to use generating functions to find the number of solutions of this equations:
u1 + u2 + ... + u7 = 16, where 1<= ui <= 5 and i= 1, ..., 7. (I've also included a screenshot of the question for more clarity.
https://gyazo.com/0b1922b9c01d99487e095353aca5a079
So I know I have sample solutions for similar questions but I can't follow their working. Here is a sample solution: https://gyazo.com/babd84f939d4a8df3c83730c5ef4e802
I can do all the way up line 5 of the solution section but I don't understand how g(X) returns that function and then also how do they get the solution from g(X) ???
Thanks a lot in advance!
Hint: consider $(u+u^2+...+u^5)^7$, specifically the coefficient in front of $u^{16}$.