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

[EX Q]: Problem: in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 160 girls , the total number of students in the college is ? 
Options: a ) 562 , b ) 356 , c ) 452 , d ) 416 , e ) 512
[EX A]: d

[EX Q]: 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
[EX A]: e

[EX Q]: Problem: 6 ) a marketing firm determined that , of 160 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ? 
Options: a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 40 , e ) e ) 5
[EX A]:
e