# Given a random distribution of matter in the universe, what's the frequency of permutations of ordered matter?

I know matter isn't purely randomly distributed since it clumps together from various forces acting on it constantly, but I just want to discuss randomly distributed matter. Unless, there is a way to incorporate clumping into the equation?

To specify, what I mean is that on average a permutation of 5 atoms would occur every some distance in the universe. But if I wanted to encounter a permutation of 6 atoms, then that would occur only once every 6 times the distance of the previous 5-atom permutation. A 7-atom permutation would be 7 times rarer than the 6-atom permutation, and so on where a permutation of 10^20 - 1 atoms would occur 10^20 times less frequently than the permutation of 10^20 - 1 atoms.

Is this a correct way of thinking? Does this have any significance? For ex, (independent) intelligent life would be so spread out that they would effectively be in different observable universes and never encounter each other. That's the motivation behind my question; I have a gut instinct that we will never meet aliens because permutation space explodes geometrically, while volume only explodes cubically and there's little reason to assume that, on large scales, permutations of matter isn't randomly distributed.