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 3 of 7 candidates eligible to fill a position in the mathematics department and 5 of 8 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 ) 42232 , b ) 42170 , c ) 14008 , d ) 16510 , e ) 41160

SOLUTION: e

PROBLEM: Problem: teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 156 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 178.50 , d ) rs . 258.50 , e ) none of these

SOLUTION: c

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

SOLUTION:
d