GMAT Problem Solving (PS) | Re: A wooden cube whose edge length is 10 inches is composed of

Though this question can be done better the way already discussed, Let's count the number of cubes with 1-face, 2-faces and 3-faces painted. This might give us a better picture if the question is modifies as : probability of getting a cube with exactly 2 faces painted or exactly 3 facespainted.

1-face painted:

Cubes with one face painted lies on each face except along the edges of the face.
So total number of 1-face painted cubes = 8*8*6 = 384<when we exclude edges, we are left with 8*8><6
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