The 57 does include mirrors. rotations make do difference, just AUFs. without mirrors, I think there is 41 OLLs.
Anonymous explained the correct answer a few posts back. and he explained it properly.
There is 5 that are 108 and 4 of them are double headlight ones. Of the two cases were everything is solved but two edges, I would think they would both have the same probability, but they do not. That is another confusing thing. Next semester when I am in statistics class, I might figure out the math behind this stuff, lol.