In this task, you need to provide the correct option for a given problem from the provided options.
--------
Question: Problem: a certain university will select 2 of 6 candidates eligible to fill a position in the mathematics department and 3 of 5 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 ) 150 , d ) 165 , e ) 315

Answer: c

Question: Problem: 8 men and 2 boys working together can do 4 times as much work as a man and a boy . working capacity of man and boy is in the ratio
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 1 , d ) 2 : 3 , e ) none of these

Answer: a

Question: Problem: at the faculty of aerospace engineering , 312 students study random - processing methods , 234 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 430 , b ) 434 , c ) 438 , d ) 444 , e ) 446

Answer:
b