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The 3 Inch Cube Riddle

A 3 inch cube is painted on all sides with RED. The cube is then cut into small cubes of dimension 1 inch. All the so cut cubes are collected and thrown on a flat surface. What is the probability that all the top facing surfaces have RED paint on them?
Hint: Visualize the core of the cube.

The core of the 3 inch cube when cut, has all faces that are not painted. Hence at least one cube with no painted face always occurs.
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