Question

A “Remski Deck” is a deck of cards consisting of nine cards in each of 10 denominations, A, 2, 3, 4, 5, 6, 7, 8, 9 and 10. In each denomination there are three cards in each of the three suits Harps: (H), Scythes (S) and Roses (R). So there are three different 2H, three different 10S, etc. for a total of 90 cards. A “hand” of eight cards is dealt. In a hand, the order the cards are dealt do not matter, and the cards of the same denomination and suit are indistinguishable. A hand is a “pair” if there are two cards of the same denomination and none of the other cards in the hand have the same denomination as the pair or each other. A “straight” consists of 8 cards in numerical order. A “flush” consists of all 8 cards from the same suit. Answer the questions below leaving your answers as combinatorial expressions. (a) How many hands contain exactly one pair? (It does not matter if the hand is also a straight or flush). (b) How many hands are straights? (It does not matter if the hand is a flush or a pair). (c) How many hands are flushes but not straights? (The hand can contain pairs).

Answer 1