How do you solve a Generating function for the number of integer solutions with no computer?
Use a generating function to solve the number of integer solutions for $$x_1+x_2+x_3=17$$
Where $2\leq x_1 \leq 5, 3\leq x_2 \leq 6, 4\leq x_3 \leq 7$
Now all this takes is doing: $$(t^2+\dots+t^5)(t^3+\dots+t^6)(t^4+\dots+t^7)$$ and looking at the coefficient of $t^{17}$. In the assignments they always asked us to just comute this using Mathematica/Maple/Matlab etc. This is no problem.
But here it is a highly marked (past)final exam question and obviously I won't have a computer.
Is there some method I don't know for solving this by hand, that explains why it is worth so many marks.
Otherwise I can't see why I am not just doing this by hand for a few minutes.