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Suppose you have a by by cube. It is painted on all six faces and then cut apart into pieces, each a by by cube. If one of the cubes is chosen at random, what is the probability that:

  1. Three sides are painted?

    This cube will have three sides painted. How many cubes like this are there in the figure? How many by cubes are there altogether? 


  1. Two sides are painted?

  1. One side is painted?

    How many cubes have one side exposed?

  1. No sides are painted?

    How many cubes have , , or sides painted? How many are left?