1. The problem statement, all variables and given/known data The integers 1 through 6 appear on the six faces of a cube, one on each face. If three such cubes are rolled, what is the probability that the sum of the numbers on the top faces is 17 or 18? 2. Relevant equations Probability = # of desired outcomes / total # of outcomes The total number of outcomes is 6*6*6 = 216. The number of desired outcomes depends. There could be 2, or 4. This is indisputable: 6, 6, 6 => 18 BUT ... 6, 6, 5 => 17 6, 5, 6 => 17 5, 6, 6 => 17 are the above sets distinguishable? Does AAB = BAA (combination)? Or is this a permutation problem, where AAB ≠ BAA? 3. The attempt at a solution If this is a combination problem, the answer is 1/108. There is one way to get 18, and one way to get 17. If this is a permutation problem, the answer is 1/54 (there are 3 unique ways to get 17 and one way to get 18). Which one is correct? I think this question just screams AMBIGUOUS, but my teacher doesn't agree with me. We were covering permutations and combinations today in my Pre-Calc class, and my teacher keeps insisting the answer is 1/54, but I can see an argument for both sides. The answer key also says 1/54, but I think that's wrong. It should be both 1/108 and 1/54 given the open-ended nature of this question (as it is currently worded).