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There are 1287 possible 5 card Poker hands that contain only diamonds, i.e. a diamond flush.

This is 13! / (13-5)! / 5!

Since there are 2598960 possible 5 card poker hands, 52! / (52-5)! / 5!, the probability of drawing a diamond flush is 1287 in 2598960, or about 0.0004952.

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Q: How many 5 card poker hands contain only Diamonds?
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