3**26 -- the number of 3 letter combinations -- is bigger than 1.8 million.
Is being "random" what's important? Or do they just need to be unique? If you need 1.8 million unique strings then you could simply use the values "1" through "1800000". Obviously, those won't be random. If you want characters rather than numbers, look into BigInteger using a radix of 26, or code something yourself. You could also look into class java.util.UUID, although I doubt those are designed to be random, per se.