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

Example Input: 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
Example Output: c

Example Input: Problem: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 27000 . what will be the ratio in which they should share the profit at the end of the year ? 
Options: a ) 20 : 9 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 5 : 3
Example Output: a

Example Input: Problem: in the class of 50 students , 30 speak tamil and 40 speak telugu . what is the lowest possible number of students who speak both the languages ? 
Options: a ) a ) 8 , b ) b ) 10 , c ) c ) 20 , d ) d ) 30 , e ) e ) 32
Example Output:
c