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A poker deck consists of fifty-two cards, representing thirteen denominations (2 through ace) and four suits (diamonds, hearts, clubs, and spades). A five-card hand is called a flush if all five cards are in the same suit but not all five denominations are consecutive. Pictured below is a flush in hearts. Let N be the set of five cards in hearts that are not flushes. How many outcomes are in N

Answer :

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Answer:

10

Step-by-step explanation:

Let N represent the set of 5 hearts cards that are not flushes

From the image attached below; there are thirteen (13) denominations on deck

i.e.  (A,K,Q,J,10,9,8,7,6,5,4,3,2) in the deck

Let us take an integral look at the set of cards that contains consecutive dominations in hearts. Relating them from the lowest denomination to the highest denomination. Also, for hand to be in a straight all cards, they must be in consecutive order.

So, starting from the lowest straight A-2-3-4-5 to the highest straight, we would have a royal flush 10, J, Q, K, A

∴

[tex]N = \left \{ {{(A,2,3,4,5,),(2,3,4,5,6),(3,4,5,6,7),(4,5,6,7,8)(5,6,7,8,9)} \atop {(6,7,8,9,10),(7,8,9,10,J),(8,9,10,J,K),(9,10,J,K,L),(10,J,Q,K,A)}} \right. \}[/tex]

Hence, the total no of outcome for N = 10

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