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In a survey of university students, 64 had taken Drama course, 94 had taken Dance course, 58 had taken a Singing course, 28 had taken Drama and singing course, 26 had taken Drama and dance course, 22 had taken Dance and singing course, and 14 had taken all the three courses. Find how many have taken only one course?

In a survey of university students, 64 had taken Drama course, 94 had taken Dance course, 58 had taken a Singing course, 28 had taken Drama and singing course, 26 had taken Drama and dance course, 22 had taken Dance and singing course, and 14 had taken all the three courses. Find how many have taken only one course? Correct Answer 106

Given:

Students who took Drama course = 64

Students who took Dance course = 94

Students who took Singing course = 58

Students who took Drama and Singing course = 28

Students who took Drama and Dance course = 26

Students who took Dance and Singing course = 22

Students who took all three courses = 14

Calculations:

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Students who took all three courses = 14

Students who took only Drama and Singing course = 28 – 14 = 14

Students who took only Drama and Dance course = 26 – 14 = 12

Students who took only Dance and Singing course = 22 – 14 = 8

Students who took only Drama course = 64 – (14 + 14 + 12) = 24

Students who took only Dance course = 94 – (12 + 14 + 8) = 60

Students who took Singing course = 58 – (14 + 14 + 8) = 22

∴ Total number of students who had taken only one course are

⇒ 24 + 60 + 22

⇒ 106

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