Stud question

[boondockst]

Hand 1: Xc Xh Xc
Hero : Xc Xc Xc

What are the odds that Hand 1 will make a club flush to beat your ass?

[elitegimp]

There are 8 clubs left in the 46 card deck. Hand 1 needs to be dealt 3 or 4 clubs in the next for cards to hit the flush, and there are 46 choose 4 = 163185 ways to be dealt 4 cards out 46.

There are (8 choose 3)*38 = 2128 ways for him to be dealt 3 clubs and 1 non-club, and (8 choose 4) = 70 ways for him to be dealt 4 clubs. Hence there are 2198 ways for him to hit the flush out of 163185 ways to be dealt 4 cards.

So the answer is 2198/163185 or 0.0135 (1.35% chance it happens), or 73.25:1 against