Question

A radio station surveyed $190$ students to determine the types of music they liked. The survey revealed that $114$ liked rock music, $50$ liked folk music and $41$ liked classical music, $14$ liked rock music and folk music, $15$ liked rock music and classical music, $11$ liked classical music and folk music, $5$ liked all the three of music.
Find:
(i) How many did not like any of the $3$ types?
(ii) How many liked any two types only?
(iii) How many liked folk music but not rock music?

Answer 1

Total number of students $=190$
Let $R,F,C$ denote set of students like rock music, folk music and classical music respectively.
(i) The number of Students not like any of the $3$ types
$=190-(90+9+5+10+30+6+20)$
$=190-170=20$
(ii) The number of Students like any two types only.
$=9+6+10=25$
(iii) The number of Students like folk music but not rock music
$=30+6=36$