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

Example Input: Problem: a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 80 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ? 
Options: a ) 3 / 16,000 , b ) 1 / 8,100 , c ) 1 / 600 , d ) 1 / 90 , e ) 2 / 45
Example Output: c

Example Input: Problem: two family reunions are happening at the same hotel , the dates reunion and the hall reunion . all 50 guests at the hotel attend at least one of the reunions . if 50 people attend the dates reunion and 60 people attend the hall reunion , how many people attend both reunions ? 
Options: a ) 2 , b ) 5 , c ) 10 , d ) 16 , e ) 60
Example Output: e

Example Input: Problem: the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 200 liters of water , how many liters of detergent will it contain ? 
Options: a ) 60 , b ) 55 , c ) 50 , d ) 45 , e ) 40
Example Output:
e