instruction:
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 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
answer:
c


question:
Problem: the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 7 : 5 : 3 . someone removes 5 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ? 
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
answer:
d


question:
Problem: in a colony of 70 resident s , the ratio of the number of men and women is 4 : 3 . among the women , the ratio of the educated to the uneducated is 1 : 4 . if the ratio of the number of education to uneducated persons is 8 : 27 , then find the ratio of the number of educated and uneducated men in the colony ? 
Options: a ) 1 : 9 , b ) 1 : 6 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 ratio 3
answer:

e