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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.