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

[Q]: Problem: ashley paid 5 dollars for 1 notebook and 1 pencil . if both prices were integers , how many pencils did ashley buy if she paid 93 dollars for the pencils and for 15 notebooks ?
Options: a ) 6 . , b ) 16 . , c ) 18 , d ) 21 , e ) 26
[A]: d

[Q]: 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
[A]: c

[Q]: Problem: there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability w that the both positions will be taken by members of just one party ?
Options: a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2
[A]:
d