Question 199708
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My apologies to rfer(78), but I must point out that his/her solution to this problem is incorrect.


There are exactly 4 five card hands that fit the criteria for a royal flush, that is, an Ace-high straight flush, namely 10-J-Q-K-A in each of the four suits.


The number of possible 5 card hands that can be dealt from a standard 52 card deck is the number of combinations of 52 things taken 5 at a time:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ _{52}C_5 = \frac{52!}{5!(52-5)!} = 2,598,960]


So the probability of a royal flush is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{4}{2,598,960} \approx 0.00000154 = 0.000154%]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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