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

Example Input: Problem: two vessels contains equal number of mixtures milk and water in the ratio 4 : 2 and 5 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ? 
Options: a ) 3 : 1 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 15 : 4
Example Output: a

Example Input: Problem: a certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 10 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 ) 70 , c ) 140 , d ) 180 , e ) 315
Example Output: d

Example Input: Problem: in a certain alphabet , 16 letters contain a dot and a straight line . 30 letters contain a straight line but do not contain a dot . if that alphabet has 50 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ? 
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 20
Example Output:
a