(13x12x11x13x12)/ (5x4x3x2x1) = 1859
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13 13 # of poker hands with 3 clubs & 2 heards = ( ) ( ) 3 2 = (13!)( 13!) / (10!*3!*11!*2) = (13!)( 13!) / (10!*11!*12) = (13!)( 13!) / (10!*12!) = 13 * 13* 12 * 11 = 22308 #
2
three
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.
There are 2597673 such hands.There are 2597673 such hands.