Roll three distinguishable dice (e.g., assume that there is a way to tell them apart, for instance, that the dice are three different colors). There are 6 × 6 × 6 = 216 possible outcomes.
For 3 < j < 18, define Aj as the event that the sum of the dice equals j. Find |Aj|, i.e., the number of outcomes in Aj? (For instance, \As\ = 1 since A3 contains only the one outcome (1, 1, 1). Similarly, |A18| = 1 since A\g contains only one outcome, (6, 6, 6).)