A full house is a five-card poker hand in which three of the values match each other and the other two values match each other (but not the first three) as well. An example: 5 50 50 AO A. The order in which the cards are dealt or laid out does not matter. (a) How many full house hands are there in a standard deck with 13 values in 4 suits? Show your work. (b) How many full house hands are there in a nonstandard deck with 16 values in 5 suits? Show your work. (c) To the 16-values-in-5-suits deck, add a Joker that functions as a wild card. The rule is that in any hand, the Joker must be interpreted in a way that will give the hand its highest possible rank. (The only part of the ranking that you need to know for this problem is that a four-of-a-kind beats a full house, and a full house beats a three-of-a-kind and a two-pair hand.) How many full house hands-including the Joker or not-are there in the new expanded nonstandard deck? (Before you begin, think about whether this final answer ought to be greater than or less than the answer to the previous item.) 22222222