[LetYouDown]

First question, depends on whether you're saying 3 of a kind or at LEAST 3 of a kind. Most people want a full house included, so here goes. Say you hold 7-7.

50 C 3 possible flops

48 C 3 possible flops without either of the 7's.

So 48 C 3/50 C 3 is the probability you won't hit a set, so subtract from 1:

1 - 48 C 3/50 C 3 = 1 - 17296/19600 = 11.755102% or 1 in 8.506944444 or about 7.5 to 1.


The second question can be solved the same way as above essentially.


For the third question. Say you hold 7-5 and the flop comes K-8-4, no flush possible.

47 C 2 possible combinations coming on turn/river.

43 C 2 possible combinations without at least one 6.

1 - 43 C 2/47 C 2 = 16.466235% or about 1/6.07 or roughly 5 to 1.