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

Example Input: Problem: if x and y are both odd prime numbers and x < y , how many distinct positive integer q factors does 2 xy have ? 
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Example Output: d

Example Input: Problem: 20 balls are numbered 1 to 20 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ? 
Options: a ) 7 / 30 , b ) 3 / 14 , c ) 9 / 38 , d ) 4 / 21 , e ) 5 / 26
Example Output: c

Example Input: Problem: a certain university will select 1 of 5 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 ) 165 , e ) 225
Example Output:
e