instruction:
In this task, you need to provide the correct option for a given problem from the provided options.
question:
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
answer:
e


question:
Problem: there are two positive numbers in the ratio 4 : 8 . if the larger number exceeds the smaller by 16 , then find the smaller number ? 
Options: a ) 25 , b ) 20 , c ) 77 , d ) 88 , e ) 44
answer:
b


question:
Problem: if 75 % of a boys answered the first question on a certain test correctly , 55 % answered the second question on the test correctly , and 20 % answered neither of the questions correctly , what % answered both correctly ? 
Options: a ) 10 % , b ) ( 8 ) 20 % , c ) 50 % , d ) 60 % , e ) 65 %
answer:

c