Poker is a card game where certain 5-card hands are better than others. these hands are simply 5-element subsets of a standard deck of 52 cards, where each card has one of 13 possible ranks and one of 4 possible suits: the 13 ranks are 2, 3, . . , 10, jack, queen, king, and ace, and the 4 suits are ♠ (spades), ♥ (hearts), ♣ (clubs), and ♦ (diamonds). each of the 13 × 4 = 52 combinations appears once in the deck. there is much already known about poker hands, so local card shark joe kerr invented a new game, pokerer, where each player gets 6 cards instead of 5. he likewise introduced new kinds of 6-card hands; joe compute how (un)common they are! for each part, count the number of 6-card hands that satisfy the specified condition, and justify your answer. you may leave your numerical answers unevaluated: arithmetic, factorials, and binomial coefficients are fine to leave in. for example, the total number of 6-card hands may be expressed as 52·51·50·49·48·47/6! (by choosing 6 cards in order and then using the division rule), or equivalently as the binomial coefficient.