The code I was referring to would just be a brute force calculation: pick 3 randomly from the group of 17 a billion times or so and output the percentage it met the 2+ req. It wouldn't help solve it analytically.
The solution where you got ~20% over constrained the problem. It gave the odds...
I know this isn't a math forum, but I just read all this and the discussion went on so long I feel the need to post the right answer... so if anyone still cares:
45.59%. Not going to include a proof, but it can be validated with a few lines of code.