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

SOLUTION: c

PROBLEM: Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 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 4 candidates are there to fill the 4 positions ? 
Options: a ) 420 , b ) 770 , c ) 840 , d ) 165 , e ) 315

SOLUTION: c

PROBLEM: Problem: what number has a 4 : 1 ratio to the number 100 ? 
Options: a ) 40 , b ) 200 , c ) 400 , d ) 800 , e ) 4000

SOLUTION:
c