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I do not get the result at this page, ex. 13-7:

Suppose that Aces can be either high or low; that is, that {Ace, 2, 3, 4, 5} is a straight, and so is {10, Jack, Queen, King, Ace}. The number of ways of getting a five card hand that is a straight flush from a standard deck of cards is:

The result is 36. However I got 40 following this approach:

I have 10 starting cards, from Ace to 10, and 4 suits, so I thought to have 40 subsets:

Ace, 2, 3, 4, 5
...
10, Jack, Queen, King, Ace

for each one of the 4 suits. Where am I doing wrong?

Thanks

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    $\begingroup$ Note that definitions can differ. Wikipedia in its definition section includes the Royal flush among the straight flushes. That gives $40$. But someone else could be using a different definition. $\endgroup$
    – André Nicolas
    Commented Jun 17, 2014 at 15:18

2 Answers 2

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If OR is exclusive in the question, meaning that Ace can either be high or low but not both would give you 36 possible combinations. However the question isn't exactly stated in a way that makes it easy to interpret this. Your logic is right though, and it could be an error on your sources part. The possible combos are

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

6 7 8 9 10

7 8 9 10 J

8 9 10 J Q

9 10 J Q K

10 J Q K A

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You have not done anything wrong, but you may be misinterpreting the 36.

  • The number of straight flushes that are not a royal flush is 36. For example, this is the number reported by Wikipedia.

  • The number of straight flushes including the royal flush is 40.

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