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counting and probability intermediate

Problem

A solid 6-by-6-by-6 cube is constructed from unit cubes and the entire outer surface is painted. What fraction of the unit cubes has at least two painted faces? Express your answer as a common fraction.
Solution
The corner cubes and edge cubes are the only ones with at least two painted faces. There are edge cubes and corner cubes, for a total of out of . The fraction is
Final answer
\frac{7}{27}