$$u_1+u_2+...+u_7 = 23$$ Where $$ 1\le u_i \le 7 =1,...,7 $$ So far, I've gotten up to the point where you actually find the generating function. so from my understanding so far there are 7 integers which must sum to 23 and lie between 2 and 6, I need to find the coefficient of 23 in:
$$(x^1 +...+x^7)^7$$ Then I get stuck here: $$x^7(1+...+x^6)^7$$ After this point i'm not sure how to get the generating function and solve the question! Any help would be greatly appreciated!