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

[Q]: Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 17 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?
Options: a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 27 / 100 , e ) 9 / 100
[A]: d

[Q]: Problem: a student committee on academic integrity has 90 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
[A]: d

[Q]: Problem: find the ratio in which rice at rs . 7.30 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 2 : 0 , b ) 2 : 3 , c ) 3 : 5 , d ) 2 : 2 , e ) 2 : 8
[A]:
c