A certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?  Pick one:  A) 81  B) 82  C) 84  D) 86  E) 88

Rationale: 1 c 4 * 2 c 7 = 4 * 21 = 84 the answer is ( c )
Answer: C