In a graded assignment the question asks:
Find a generating function for $ar$, the number of ways a roll of six distinct dice can show a sum of $r$ if: The first three dice are odd and the second three even.
It's been marked but I'm quite certain the lecturer is incorrect.
My answer is : $$(x+x^3+x^5)^3 . (x^2+x^4+x^6)^3$$
Am I correct that my lecturer is incompetent? It is not the first time this guy has done this. I want to lay a formal complaint.