Each of five, standard, six-sided dice is rolled once. Two of the dice come up the same, but the other three are all different from those two and different from each other. The pair is set aside, and the other three dice are re-rolled.
The dice are said to show a "full house" if three of the dice show the same value and the other two show the same value (and potentially, but not necessarily, all five dice show the same value). The dice are said to show "four of a kind" if at least four of the dice rolls are the same.
What is the probability that after the second set of rolls, the dice show a full house or four of a kind?
