A large cube 10 cm on a side is composed of cubes 1 cm on a side. The outside of the large cube is painted red and then all of the individual cubes are mixed in a drum. If two cube is selected randomly what is the probability that first cube has exactly one red face and second has exactly two red faces?
The cube has 6 surfaces. On each surface there are exactly 8x8 or 64 cubes painted on 1 surface. Total number of cubes painted on 1 surface is therefore 64x6=384
The cube has 12 surface edges. On each surface edge, there are 8 cubes that are painted red on 2 surfaces. Total = 8x12=96
Therefore the prob = 384/1000 x 96/999