Task: Question Answering
Input (English): Problem: a certain university will select 3 of 7 candidates eligible to fill a position in the mathematics department and 5 of 8 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 ) 42232 , b ) 42170 , c ) 14008 , d ) 16510 , e ) 41160
Output (English): e