Odds of set over set

[KegNog]

I was playing 6 handed hold'em on fulltilt poker where i was dealt 77 on the button. There were 3 people in the pot and the flop comes down K-7-10. I'm loving this, but when the action gets to me, the BB has bet pot, and the MP player has reraised the pot...I go all-in (I have them both covered) and get called by BOTH!!! BB shows KK and the other show 10-10...i'm drawing virtually dead, as are the 10's.

What is the probability of 3 people being dealt Pocket Pairs in a 6 handed game, and each person hitting his set on the flop?

I know the odds for any pair to be dealt is 220-1 and I know that the probability of hitting a set on the flop is about 11.5% (141/1225).

How do you calculate multiple hands here to find out the total probability of the occurence? The math is appreciated!

Thanks!

[LetYouDown]

Assuming you have K-K vs. 10-10 vs. 7-7. You know 6 cards. Thus, there are 46 C 3 possible flops, or 546480. There are 2 Ks, 2 Ts and 2 7s remaining in the deck. 8 of these combinations are K-T-7. By my crazy math, that makes 8/546480 or 1/68310.