A flush in poker is a hand where all five cards are of the s

A \"flush\" in poker is a hand where all five cards are of the same suit. A \"straight\" is a hand where the denominations of the five cards are in order. Typically an ace is counted either as a \"one\" or as a \"fourteen,\" so both the hands 1S, 2H, 3C, 4C, 5D and 10C, 11C. 12D, 13H, 1H are considered straights. A hand that is both a flush and a straight is a \"straight flush.\"

A) How many possible poker hands are a straight flush?
B) How many possible poker hands are a straight? (not a straight flush)
C) How many possible poker hands are a flush? (not a straight flush)
D) How many possible poker hands are two pair? (two of one denomination, two of a second denomination and one of a third denomination, such as 8D, 8C, 3S, 3D, 11D)
E) How many possible poker hands are a full house? (three of one denomination and two from a second denomination, such as 7C, 7D, 7H, 1 D, 1 S)

Can anyone help me with these questiosn ?Please if you dont know the answer or you are not sure ,please dont answer and waste me a question without anyhelp

Solution

a)

For each suit, there are 10 straight flushes.

As there are 4 suits, then there are 40 straight flushes.

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b)

There are 10 possible straights, in terms of just number.

However, each straight combination can be varied in suits in 4^5 = 1024 ways.

Thus, there are 1024*10 = 10240 straights, but this includes straight flushes.

Deducting the straight flushes,

# of straights = 10240 - 40 = 10200 [ANSWER]

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C)

There are 13C5 = 1287 ways to choose a flush for each suit.

As there are 4 suits, there are 1287*4 = 5148 flushes. [ANSWER]

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d)

For each rank you can choose 4C2 = 6 pairs.

You can choose 13C2 = 78 ranks to for 2 pairs.

From there, you can choose from the remaining 44 cards.

Hence, there are 6*78*44 = 20592 two pairs.

e)

From each rank you can choose 4C3 = 4 trios.

There are 13 ranks to choose from.

From the remaining 12 ranks, you can choose 4C2 = 6 pairs for each rank.

There are 12 ranks to choose from.

Thus, there are 4*13*6*12 = 3744 full houses. [answer]