When throwing a die $3$ times, find the probability of the product of the three results being a multiple of $9$.
I tried drawing a table for the possible outcomes of the first TWO dice. Then I tried considering the cases for each when the third die is rolled - as you can imagine not very efficient. Perhaps I could use $x+y+z = 9k$ as a divisibility test, where $k$ is an integer. I'm pretty sure this would involve stars and bars, but I'm not sure how to implement it in this case. Would I have to solve for $k$?
I also worked out the boundaries but I'm not sure if that will help either: $9≤x+y+z≤216$.
Do I need to use stars and bars for this question?