In this task, you need to provide the correct option for a given problem from the provided options.

[Q]: 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
[A]: c


[Q]: Problem: in a class , 30 students pass in english and 20 students in math , while some students among these pass in both . how many more students do only english as compared to those doing only maths ? 
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) indeterminate
[A]: a


[Q]: Problem: if the numbers 1 to 96 are written on 96 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ? 
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 96 , d ) 1 , e ) 2
[A]:
c