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 2 of 6 candidates eligible to fill a position in the mathematics department and 3 of 5 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 ) 150 , d ) 165 , e ) 315
Example Output: c

Example Input: Problem: the marks obtained by polly and sandy are in the ratio 3 : 5 and those obtained by sandy and willy are in the ratio of 3 : 2 . the marks obtained by polly and willy are in the ratio of . . . ? 
Options: a ) 3 : 4 , b ) 5 : 6 , c ) 7 : 8 , d ) 9 : 10 , e ) 11 : 12
Example Output: d

Example Input: Problem: in a neighborhood having 90 households , 11 did not have either a car or a bike . if 18 households had a both a car and a bike and 44 had a car , how many had bike only ? 
Options: a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10
Example Output:
b