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How many possible positions can be attained by the Rubik's cube, assuming that you can pop out the corners and edges and place them where you like but not the centres?

How many possible positions can be attained by the Rubik's cube, assuming that you can pop out the corners and edges and place them where you like but not the centres?

Yes, all the corners and edges must be placed back into the cube. Is the answer really that simple? I thought maybe I was being simple minded when I thought it was just 12 x 43 quintillion

Yeah, it's just that. The more mathematical way to calculate it is
(corner possibilities)*(edge possitibilities)
= (8! 3^8)*(12! 2^12) = 5.19024039 x 10^20.

You mean an extra factor of 30. When you fix a corner or edge there are 24 ways to fix centers if you're not allowed to move the center caps; if you can move the center caps there are 720 ways.