Suppose you roll three 4-sided dice to arrive at one of 64 combinations.
Of these 64 combinations, 40 are "good," 15 are "bad," and 9 are "mixed."
You have to repeat the process three times, which makes for ten possible outcomes, e.g., 3 good; 2 good and 1 mixed; 2 good and 1 bad, etc. down to 3 bad.
What are the probabilities of each of the ten possible outcomes, given that one is more likely to receive a good combination (.625) versus a mixed (.14) or bad (.23) combination? What is the formula?
(In case you're wondering, this problem arises from a form of dice divination practiced in India and elsewhere with long dice called pashakas.)