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2-41.

Suppose you have a 3 by 3 by 3 cube. It is painted on all six faces and then cut apart into 27 pieces, each a 1 by 1 by 1 cube. If one of the cubes is chosen at random, what is the probability that: Homework Help ✎

  1. Three sides are painted?

    This cube will have 3 faces painted. How many cubes like this are there in the figure? How many cubes are there altogether?

    cube

  2. Two sides are painted?

  3. One side is painted?

    How many cubes have one face exposed?

  4. No sides are painted?

    How many cubes have 1, 2, or 3 faces painted? How many are left?