Four players each are dealt one card. In how many ways could the four dealt cards all be clubs or honor cards?

Question

Honor cards include all the 10s, Jacks, Queens, Kings, and Aces.

Answer 1

There are 13 clubs and 5 honors in the other 3 suits, so there are 13 + 5*3 = 13 + 15 = 28 cards to choose from. There are 52 cards total. Then, the chance of 4 players selecting all clubs or honors is

C(28,4)/C(52,4) = P(28,4)/P(52,4) = 28*27*26*25/(52*51*50*49) = 4*7*3*9*26*25/(2*26*3*17*2*25*7*7) =

9/(17*7) = 9/119 = .0756