Combinatorics Olympiad Problem 6

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 of this large cube is completely red? Express the answer as a decimal (you will certainly have to use scientific notation!).

This problem is not original.This problem is part of this set.

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