[BruceZ]

Here's the exact solution.

It's much easier if you first consider the odds of getting any 3 different cards on the flop, that's
52*48*44/(52*51*50). Then multiply this by the probability that the 3 pairs are out that match the 3 cards on the flop. Note that no more than 1 player can hold each of the pairs and there are 3 ways to hold each one. The probability of 3 specific players holding these pairs is 9/C(49,2) * 6/C(47,2) * 3/C(45,2). Finally, there are C(10,3) ways to choose the 3 players. Putting it all together we have:

52*48*44/(52*51*50)*9/C(49,2)*6/C(47,2)*3/C(45,2)*C(10,3) = 0.0013% or 1 in 78,166.