A certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 4 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?	Options.
A) 42	B) 70	C) 175	D) 165	E) 315
51751*71754 = 5*35= 
<gadget id="calculator">5*35</gadget>
<output>175</output>
175   the answer is (175)
<result>C</result>
A certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 4 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?