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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?

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Solution

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)
=190170=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

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