Find the number of ways to distribute 19 identical computers to four schools, if School A must get at least three, School B must get at least two and at most five, School C get at most four, and School D gets the rest.
a) Solve using inclusion-exclusion
b) Solve using generating functions
I've been tackling this question for a couple of days and I am pretty confused where to even start.
So I bet the answer is in the form $x_1 + x_2 + x_3 + x_4 = 19$, where $x_1 \ge 3; 2 \le x_2 \le 5; x_3 \le 4$ and $x_4$ is whatever is left over.
And then I get confused. I've looked all over the internet, through textbooks and I'm not getting anywhere. Any help would be appreciated, thank you.