[BruceZ]

This was supposed to be easy, not an exercise in looking up published numbers. Let me clarify:

[ QUOTE ]
Count the number of ways to make such a hand, without regard to the order of the cards, and divide by the total number of possible hands C(52,5) = 2,598,960. Consider the number of possible denominations for the set <font color="red">12</font>, the number of ways to make a set for each denomination <font color="red">4</font>, and the number of ways to get the other 2 cards <font color="red">4*4</font>.

[/ QUOTE ]

The numbers in red above assume AAA2K is not allowed, but 222A3 and KKKQA are allowed. Otherwise change the number 12 accordingly.

12*4*4*4 / 2,598,960 =~ 0.03% or 1 in 3384

Done.