Question: Please answer the following question Problem 7 (Counting) (10 points). In a standard 52-card deck (13 ranks and 4 suits), a hand is a 5-card

Please answer the following question

Problem 7 (Counting) (10 points). In a standard 52-card deck (13 ranks and 4 suits), a hand is a 5-card subset of the set of 52 cards. Express the answer to each part as a formula using factorial, binomial, or multinomial notation. (a) Let Hyp be the set of all hands that include no pairs; that is, no two cards in the hand have the same rank. What is | HNP|? (b) Let Hy be the set of all hands that are straights, i.e. the ranks of the five cards are consecutive. The order of the ranks is (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, k, A); note that A appears twice. What is | Hs |? (c) Let HF be the set of all hands that are flushes; that is, the suits of the five cards are identical. What is | HF |? (d) Let HSF be the set of all straight flush hands; that is, the hand is both a straight and a flush. What is | HSF |? (e) Let HAC be the set of all high-card hands; that is, hands that do not include pairs, are not straights, and are not flushes. What is | HHC|

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