5. Laura paints the entire surface of a wooden cube blue, then cuts it into $6^{3}=216$ equal smaller cubes. By mixing the smaller cubes and randomly picking one, what is the probability that Laura finds one with exactly two blue faces?
(A) $8 / 27$
(B) $1 / 6$
(C) $1 / 4$
(D) $4 / 9$
(E) $2 / 9$
Problem 5. The correct answer is (E).

Along each of the edges of the cube, there are 4 small cubes with two faces painted blue. These constitute all the small cubes with two blue faces, and moreover, the different groups of 4 small cubes arranged along the edges are pairwise disjoint. Since the edges of a cube are 12, there will be $12 \cdot 4=48$ small cubes with two blue faces. The probability of drawing one is therefore $\frac{48}{6^{3}}=\frac{2}{9}$.