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This could be extremely complex. You can't just take all the possible positions for a single piece and multiply them times all the possible positions for every other piece because some combinations wouldn't be possible to create in a game, the possible positions of the king for example would be limited depending on the positions of the other pieces. Also every single pawn has the possibility of reaching the opposite rank and therefor being promoted so you also have to deal with the possibilties of multiple queens.
In fact the pawns add tremendous complexity to the problem since they can't pass each other but through taking other peices it is possible for them to end up many ranks left or right of their initial position but only when they aren't close or next to a board edge.
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