What are the odds of pulling 3 1984 quarters out of a pile?

Chances of pulling 3 1984 coins

"Picked up 3 quarters from my spare change pile. They were all from 1984. What are the 
chances?!?!" [http://d.pr/9Trc]

So first, we need to figure out how many quarters in any given pile should be dated 1984. 
Let's say that there are 65 billion quarters in circulation at the moment [1] and that 
there were 1.2 billion quarters minted in 1984 [2].

That means that 1.85% of the quarters in a given pile should be quarters with the date 
1984. [1.2/65 = 1.85%]

Assuming an absurdly large pile of 1000 quarters, 18.5 should be dated 1984. We'll 
drop the .5 and call those the coins taken out of circulation between 1984-2012. 
Now it's time to pick the quarters.

The first pick has a 18/1000 chance of getting an '84 coin.
Second, 17/999.
Third, 16/998.

18    17   16   = 4,896         / 4896  =  1
1000  999  998  = 997,002,000   / 4896  =  203,636

So what are the odds of pulling 3 1984 quarters out of pile? My best guess is 1 in 203,636. 

Give or take.




[1] http://www.fluther.com/25214/how-many-us-quarters-exist/
[2] http://www.coincommunity.com/us_quarter_dollars/washington.asp 
   (676,545,000 + 546,483,064 = 1,223,028,064.)