Question 523120: I've tried this numerous of time but I just can't figure it out. A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the specified type. Straight (five cards of consecutive denominations: A, 2, 3, 4, 5 up through 10, J, Q, K, A, not all of the same suit) (Note that the ace counts either as a 1 or as the denomination above king.)
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
The straights are these 10
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
and for each of those 10 ways, the 5 cards
can have any of 4 suits each, so the
total number of hands in sequence is 10×4×4×4×4×4 = 10×45 = 10240
However this 10240 contain the straight flushes in which all
five cards have the same suit, so we must subtract the straight
flushes. To find the number of straight flushes, we can choose
the sequence any of 10 ways and the common suit any of 4 ways,
so that's 10×4 or 40 straight flushes we must subtract from the
10240, so the answer is 10240-40 or 10200.
Edwin
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