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

Problem: what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ?
Options: a ) e = 5 , b ) e = 9 , c ) e = 10 , d ) e = 20 , e ) 30
d

Problem: a bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 7 / 16 , b ) 7 / 12 , c ) 7 / 19 , d ) 7 / 12 , e ) 7 / 15
e

Problem: 30 liters of a mixture contains milk and water in the ratio 2 : 1 . if 5 liters of this mixture be replaced by 5 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 3 : 2 , b ) 3 : 1 , c ) 4 : 1 , d ) 5 : 2 , e ) 2 : 1
d