TASK DEFINITION: In this task, you need to provide the correct option for a given problem from the provided options.
PROBLEM: Problem: what is the greatest value of x such that 4 ^ x is a factor of 21 ! ? 
Options: a ) 5 , b ) 6 , c ) 3 , d ) 2 , e ) 4

SOLUTION: b

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: in a sports club with 27 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ? 
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11

SOLUTION:
e