Math Help - Difficult probability problem

A large white cube is painted red, and then cut into 27 identical smaller cubes. These smaller cubes are shuffled randomly. A blind man (who also cannot feel the paint) reassembles the small cubes into a large one. What is the probability that the outside if this large cube is completely red?

there are 4 types of subcube:

those with no sides painted (1)
those with 1 sides painted (6)
those with 2 sides painted (12)
those with 3 sides painted (8)

Any shuffling of these subcubes within their own group will keep the cube exterior completely red, so there are 1!6!12!8! possible solutions. You should allow for orientations but i think this has no effect on this part of the calc (i think that for any given position, only 1 orientation is valid).

Step two: find the total number of outcomes (including orientations) and divide one by the other.

PS: I should warn you i dont have the best track record at combinatronics problems so i might have got that spectacularly wrong

Originally Posted by SpringFan25

PS: I should warn you i dont have the best track record at combinatronics problems so i might have got that spectacularly wrong

I hope you're better at combinatorics