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? Choose the correct choice from the following:
A) 81  B) 82  C) 84  D) 86  E) 88
1844*2847 = 4*21= 
<gadget id="calculator">4*21</gadget>
<output>84</output>
84   the answer is (84)
<result>C</result>
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?