How many mistakes can be done in a puzzle of 12320 pieces?

Ale: How many mistakes can be done in a puzzle of 12320 pieces?
The puzzle has 12320 pieces from which there are 308 diferent shapes of pieces, …so each shape has 40 pieces.
and each shape can be put in the puzzle in two different positions. Can someone help to find the quantity of variations to construct the puzzle not correctly?

Answers and Views:

Answer by keysfunding
dude… this one is a tuffy:

forget about correctly vs incorrectly… let’s first talk about number of variations:

12320 pieces
2 positions for each placeable piece
40 pieces can be placed…

I might be wrong so doublecheck your answer but I think it’s 2×40! (40 factorial – since once you place one of the pieces, there are only 39 to place and so on)… 2 times accounts for the two places per piece…

The 308 different shapes doesn’t play into the formula since a particular shape can NOT be placed into the wrong shape place regardless of whether or not it belongs there.

Screw it – I have no idea but I’m going to post what I have in case it gives you a clue where to start. Good Luck!