Good point, forgot about less than 32 pieces on the board. Also I forgot about pieces being interchangable.
...Lot more complicated now 
So it'll be (32piece positions+31piece positions...+2piece positions)*2 for whose move it is
Ignoring illegal moves for now,
32P:(64!/32!(8!2!2!2!)*2) ~7.475 × 1047
31P: 2(64!/33!(8!2!2!2!)*2)+12(64!/33!2!(8!2!2!)*2!)+16(64!/33!8!7!(2!2!2!)*2)
~4.077*10^47
The rest of it seems too much work to tackle....
And chances are, I'll make mistakes all over the place
anyway, its probably somewhere between 10^49 and 10^51.
apteryx was correct! The math is 64*63*62*61*60*59*58*57*56...34*33*32-illegal positions as he said
Also, you must multiply by the amount of different peices that can go in each square. After the two kings the third peice can be a white queen who can go in the empty spots. The piece could also be a black rook, which pretty much doubles the places that the third peice can go. Also, it could be a black knight ect.
I don't think the order that the pieces are placed matters... Only the square which they go in.
e.g chess isn't a different game if the first pice you put on the board when setting it up is the White Queen, the Black Rook, or the Black Knight.
I am not saying it matters what the order placed is. I am saying it matters what peice is placed if there are less than 32 peices on the board.