The six faces of a cube are painted black. The cube is then cut into $3^3$ smaller cubes, all the same size.

(a) How many of the smaller cubes have exactly one black face?

(b) How many of the smaller cubes do not have any black faces?

(c) One of the small cubes is chosen at random, and rolled. What is the probability that when it lands, the face on the top is black?

parmen Jun 8, 2024