# Blind Man with Cubes.

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. Let $$P$$ denote the probability that the outside of this large cube is completely red?

What is the value of $$10^{37} \times P$$? (Answer to two decimal places)

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