TASK DEFINITION: In this task, you need to provide the correct option for a given problem from the provided options.
PROBLEM: Problem: a certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 10 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 ) 42 , b ) 70 , c ) 140 , d ) 180 , e ) 315

SOLUTION: d

PROBLEM: Problem: find the number of different prime factors of 25650 
Options: a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6

SOLUTION: a

PROBLEM: Problem: a certain high school has 500 students . of these students , 40 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ? 
Options: a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470

SOLUTION:
c