If (A={1,2,3,4}) and (B={0,1,2}), how many functions from (A) to (B) have exactly (2) elements in their range?

Correct answer: (36)

First choose (2) values from (B) in (\binom{3}{2}=3) ways, and both chosen values must occur, so each pair gives (2^4-2=14). The total is (3\cdot14=42), which is not in the options.