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: the ratio of the adjacent angles of a parallelogram is 4 : 11 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ? 
Options: a ) 132 ° , b ) 228 ° , c ) 156 ° , d ) 224 ° , e ) none of these
[A]: a


[Q]: Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 8 ounces of corn syrup , how many ounces of water does it contain ? 
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 120
[A]:
e