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

Problem: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 2 : 3 and 3 : 1 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel . 
Options: a ) 99 : 61 , b ) 99 : 160 , c ) 61 : 160 , d ) 61 : 99 , e ) 99 : 160
a

Problem: a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 100 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 / 4,800 , c ) 3 / 1,600 , d ) 1 / 90 , e ) 2 / 45
b

Problem: if w is the set of all the integers between 49 and 88 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ? 
Options: a ) 11 , b ) 44 , c ) 48 , d ) 28 , e ) 26

e