What is the probability of this Rubik's cube configuration?

Question

What percentage of the total number of combinations on a Rubik's Cube have the following property:

On every face, no two adjacent squares have the same color.

By adjacent I mean:

adjacent: sharing a common side.

Answer 1

I have no idea of the exact answer. There are 72 pairs of adjacent squares, so perhaps it would be near $(5/6)^{72}$ or around 2 in a million.