Find the probability of being dealt five clubs and three cards with one card of each other remaining suit in ​8-card poker.

Answer 1

There are C(13,5) ways of selecting clubs and 13 ways of selecting a heart, a spade, and a diamond. There are C(52,8) possible 8 card hands. Thus, the probability of 5 clubs, 1 heart, 1 spade, and 1 diamond is

C(13,5) * 13³ /C(52,8) = 2827539/752538150 = 24167/6431950 = .003757