A certain university will select 1 of 7 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?  Select the correct option
A) 42  B) 70  C) 147  D) 165  E) 315

Rationale: "ans : 147 7 c 1 * 7 c 2 answer c )"
Answer: C