If the Universe is in fact infinite (as suggested by String Theory), then the arrangements of atoms or even subatomic particles is finite for any region. There must, in fact, be an infinite number of identical copies of me, typing these words, with you reading them. The nearest of these has been computed to be about 10^(10^29000) light years, in any direction from here, with lots of near copies on the way there.
I wish them luck. That's pretty selfish, really. Since they're identical, they're wishing me luck.