Final answer:
To find the probability that exactly two boxes remain empty, we need to consider the number of ways we can choose the two empty boxes. There are 5 choose 2 ways to select two boxes out of five. Once we have chosen the empty boxes, there are 3! * 5! ways to distribute the marbles. Therefore, the probability is 3/5.
Step-by-step explanation:
To find the probability that exactly two boxes remain empty, we need to consider the number of ways we can choose the two boxes that remain empty. There are 5 choose 2 ways to select two boxes out of five. Once we have chosen the two empty boxes, there are 3! = 6 ways to distribute the five marbles into the remaining three boxes. However, since the marbles are different, we need to multiply this by 5! = 120 to account for the different arrangements of the marbles.
Therefore, the total number of favorable outcomes is (5 choose 2) * 6 * 120 = 60 * 6 * 120 = 43200. The total number of possible outcomes is 5^5 = 3125. So, the probability is 43200/3125 = 3/5.