Question

In Yahtzee, 5 standard dice are rolled up to three times on a given turn. A player can choose to save anywhere from 0 - 5 of the dice between rolls 1 and 2 and between rolls 2 and 3, meaning that the player can set aside certain dice before rolling the remaining dice if they choose to do so. Suppose that a given player does not take advantage of saving die rolls and instead rolls all 5 dice each of the 3 rolls. What is the probability that the player will have at most 2 faces the same on the first roll, exactly 3 or exactly 4 faces the same of the second die roll, and a Yahtzee (all 5 faces the same) on the third die roll?

Answer 1