On The Flop: Set Over Set Over Top Two

Last month (November) I witnessed a flop that was wicked, which I don't think I've ever seen before. We all have seen set over set on the flop at least a few times, and know how unlikely that is. But how about set over set over two pair (and not just any two pair, top two)!! All three players in the hand were essentially allin on the flop, with the winner went to the player who held the best set (set of 10's).

Flop: A - 10 - 3

Player1 holds A - 10
Player2 holds 10-10
Player3 holds 3-3

Odds of that flop coming out given the three known hands:
a) Flop can come out in the following ways --> A-10-3, A-3-10, 10-A-3, 10-3-A, 3-A-10, 3-10-A
b) Each combination odds is --> (3/46 X 1/45 X 2/44) + (3/46 X 2/45 X 1/44) + (1/46 X 3/45 X 2/44) + (1/46 X 2/45 X 3/44) + (2/46 X 3/45 X 1/44) + (2/46 X 1/45 X 3/44) = 0.000066 X 6 (appx.) = 0.000395 or 0.0395% or about 4 in 10,000. Ouch!!

Odds that A - 10 will win: He needs an ace for a boat 2/43 + 2/42 = appx 9.4%
Odds that 3 - 3 will win: He needs the case 3, bummer. 1/43 + 1/42 = appx 4.7%
Odds that 10 - 10 will hold against the two other hands: 100 - (9.4 + 4.7) = 85.9%

Aside - Set over set over two pair in another type of combination -->
Say the flop is AKx and the players have AA KK and AK. What are the odds of that flop coming out given the three players' known hole cards?
We have: (1/46 X 1/45) X 6 = 0.000483 or 0.0483 or about 5 in 10,000.

As an aside, the odds of having set over set on the flop is:
Given that two players each have a pair already, the flop needs to come out with one of each of their hole cards. Say players hold JJ and 99. Thus the flop could be J-9-x or J-x-9 or 9-J-x or 9-x-J or x-J-9 or x-9-J (six combinations). Each combination is appx 2/48 X 2/47 = 0.00177 or 0.177%. Thus odds of set over set are appx 0.00177 X 6 = 1%.

As another aside, the odds of having set over set over set on the flop is:
Given that three players already have a pair, the flop needs to come out with one of each of their hole cards. 2/48 X 2/47 X 2/46 = 0.000077 X 6 = 0.00046. Thus the odds of set over set over set on the flop are appx 0.046% or almost 5 in 10,000.