A French deck of 52 cards consists of four suits (clubs, diamonds, hearts, and spades) of 13 ranks each (Ace, 2-10, Jack, Queen, King), more briefly written as (A, 2-10, J, Q, K). A poker hand consists at least one card from the deck and we treat it unordered here. (a) A flush consists of 5 cards with same suit. A straight flush consists of 5 cards with same suit and sequential rank, e.g., {A♠ , 2♠ , 3♠ , 4♠ , 5♠ }. Under high rules, Ace (typically written as A) can rank either below 2 or above King (typically written as K), but not at the same time, e.g., {A♠ , 2♠ , 3♠ , Q♠ , K♠ } is not a straight flush. How many non-straight flushes are there? (b) A straight is a poker hand containing five cards of sequential rank, not all of the same suit, such as {2♠ , 3♠ , 4q , 5♣ , 6r }. How many straights are there? (c) How many poker hands consist of cards all of the same suit?
. A French deck of 52 cards consists of four suits (clubs, diamonds, hearts, and spades) of
13 ranks each (Ace, 2-10, Jack, Queen, King), more briefly written as (A, 2-10, J, Q, K). A poker hand
consists at least one card from the deck and we treat it unordered here.
(a) A flush consists of 5 cards with same suit. A straight flush consists of 5 cards with same suit
and sequential rank, e.g., {A♠ , 2♠ , 3♠ , 4♠ , 5♠ }. Under high rules, Ace (typically written as A)
can rank either below 2 or above King (typically written as K), but not at the same time, e.g.,
{A♠ , 2♠ , 3♠ , Q♠ , K♠ } is not a straight flush. How many non-straight flushes are there?
(b) A straight is a poker hand containing five cards of sequential rank, not all of the same suit, such as
{2♠ , 3♠ , 4q , 5♣ , 6r }. How many straights are there?
(c) How many poker hands consist of cards all of the same suit?
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