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 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 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 4 candidates are there to fill the 4 positions ? 
Options: a ) 420 , b ) 770 , c ) 840 , d ) 165 , e ) 315
answer:
c


question:
Problem: if w is the set of all the integers between 19 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ? 
Options: a ) 26 , b ) 32 , c ) 33 , d ) 34 , e ) 54
answer:
e


question:
Problem: the ratio of numbers is 3 : 4 and their h . c . f is 8 . their l . c . m is : 
Options: a ) 12 , b ) 96 , c ) 24 , d ) 48 , e ) 98
answer:

b