A basket contains 6 red, 5 green and 8 blue balls. If four balls are picked at random, what is the probability that all four of them are either red or any two out of the four are green?

$nleft( E ight) = 6{C_4} + 5{C_2} imes 14{C_2}$

$Pleft( E ight) = frac{{6{C_4} + 5{C_2} imes 14{C_2}}}{{19{C_4}}} = frac{{15 + 910}}{{2876}} = frac{{925}}{{3876}}$