instruction:
In this task, you need to provide the correct option for a given problem from the provided options.
question:
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
answer:
b

question:
Problem: in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 7 : 7 : 8 . if the shop carries 330 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 42 , b ) 66 , c ) 98 , d ) 112 , e ) 154
answer:
e

question:
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 9 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 ) 252
answer:
e