Task: Question Answering
Input (English): Problem: a certain university will select 2 of 3 candidates eligible to fill a position in the mathematics department and 4 of 5 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 ) 10 , c ) 40 , d ) 65 , e ) 15
Output (English): e