A cube 4 units on each side is composed of 64 unit cubes. Two faces of the larger cube that share an edge are painted blue, and the cube is disassembled into 64 unit cubes. Two of the unit cubes are selected uniformly at random. What is the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces?
This problem is not that hard to at least start.
You need to assume that nothing is painted other than the 2 sides that are painted blue.
Think about the box before you dismantle it.
How many blocks have 2 sides painted?
How many have only one side pained.
Maybe draw the cube or even just a 4 by 4 side to help you work it out.
Come back with your answers.
Please no one answer any more until Swimm makes a proper thought-through response.