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

[EX Q]: Problem: a class has a ratio of 3 : 6 : 7 of children with red hair , blonde hair and black hair respectively . if the class has 9 kids with red hair , how many kids are there with black hair ? 
Options: a ) 7 , b ) 6 , c ) 9 , d ) 21 , e ) 63
[EX A]: d

[EX Q]: Problem: a certain university will select 1 of 6 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 ) 216 , b ) 212 , c ) 214 , d ) 210 , e ) 120
[EX A]: a

[EX Q]: Problem: a student committee on academic integrity has 72 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
[EX A]:
c