A833 Four Speed Gets Stuck in Reverse

Back from a nice wedding, and a birthday afternoon with my kids at a local brewery (Kudo's to Calicraft in Walnut Creek!!) Tonight, back under the car to check it out.

Doing the math then; there are 8x7x6x5x4x3x2x1=40320 different possible ways to assemble it.
Some of them however are intuitive, and the assembler would have to not be very bright to mix them up. Like the two short levers and the shift mech. If you call that one choice,with two choices for where the levers go; then you have (2)x5x4x3x2x1= 240 different ways left.
But if you realize that two of the shims only fit in one location each and only orient in one direction, that changes the total number of choices from 8 to 6, and so now it looks like this; (2)x3x2x1=12 different ways left...
And that wraps up today's lesson in Combinations and Permutations!