Problem #45 MEDIUM
The Painted Cube
Amazon Meta Math Pattern Recognition
Problem Statement
A solid wooden cube measuring 4 x 4 x 4 units is painted red on all six of its outer faces. It is then cut into 64 smaller unit cubes (each measuring 1 x 1 x 1). If you pick one of these 64 small cubes completely at random, what is the probability that it has paint on exactly 2 of its faces? Generalise your approach for an n x n x n cube.
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