poker <- data.frame(
  none = choose(13,5)*4^5 - 10*4^5 - 4*choose(13,5) + 10*4,
  pair = 13*choose(4,2)*choose(12,3)*4^3,
  two.pair = choose(13,2)*choose(4,2)^2*11*4,
  triple = 13*choose(4,3)*choose(12,2)*4^2,
  straight = 10*4^5 - 10*4,
  full.house = 13*choose(4,3)*12*choose(4,2),
  flush = 4*choose(13,5) - 10*4,
  four = 13*choose(4,4)*12*4,
  straight.flush = 10*4 - 4,
  royal.flush = 4)
sum(poker) - choose(52,5)
poker/choose(52,5)