Probability question 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 this probability that the outside of this large cube is completely red?

These "complex" probability questions should always be addressed in a similar manner. Decompose them in smaller subproblems and solve them separately.

This problem could be decomposed in finding these probabilities:

* probability that the inner center is in its place
* probability that the $8$ corner pieces are at the corner positions
* probability that each corner piece is correctly orientated
* probability that the $6$ center pieces are at the center positions
* probability that each center piece is correctly orientated
* probability that the $12$ edge pieces are at the edge positions
* probability that each edge piece is correctly orientated



If you find those, you can multiply all of them and get the final result.