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A straight flush is a hand that contains five cards in sequence, all of the same suit, such as Qâ£ Jâ£ 10â£ 9â£ 8â£ (a hand that meets the requirements of both a straight and a flush). Two such hands are compared by their card that is ranked highest.
How many 4-card hands are there consisting entirely of diamonds? SOLUTION: As there are 13 diamonds in a standard deck of 52 cards, we are counting the number of combinations of 4 cards chosen from the 13 diamonds in the deck. This gives 13C4 =13P4 / 4! = (13121110) / (4321) = 17160 / 24 = 715 hands consisting entirely of diamonds.