# Probability of Flush (fraction)

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"Probability"_"Flush" = [((13),(5))((4),(1))-((10),(1)) ((4),(1))]" in " ((52),(5))
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MichaelBartmess.Probability of Flush (fraction)
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The Probability of a Flush (fraction) constant defines the probability of being dealt a Flush as a fraction.  The Flush is a five card hand having all in the same suit and the card values do not have to be in consecutive order. An example of a Flush would be the following five cards all of the same suit

• a 2
• a 3
• a Queen
• a 7
• a 10

The number of Flushes possible is the product of the number of five card choices in the 13 card values, ((13), (5)) times the number of suits, ((4), (1)); minus the product of the number of royal flushes ((4), (1)) times the number of straight flushes((10), (1)).   So the chances of being dealt a Flush (excluding royal flush and straight flush) is the ratio of the number of Flushes to the total number of five card hands that are possible.  The total number of five card hands possible is computed as ((52), (5)).