Exercise

Probability of a full house

A full house occurs when three of the dice are of one denomination, and the remaining two dice are of another denomination. In other words, it consists of a "set of three" and "a pair." An example is {2,2,2,5,5}.

Let's calculate the probability of a "full house" in a single roll of the five dice.

Instructions

100 XP

Calculate the overall number of denominations possible for the set of three and the pair together.
Calculate the number of ways to form the groups; that is, which dice are in the set of three and which are in the pair.
Combine the previous two quantities to determine the number of possible full houses.
Calculate the probability of obtaining a full house, and then print it.