Question Detail
Question
In a survey of 120 students... Now, suppose 10 Students offer the three Subjects, how many dislike the three Subjects?
Correct Answer
Option B is the correct answer.
Detailed Explanation
n(M)=70, n(P)=60, n(C)=50, n(M∩P)=30, n(M∩C)=28, n(P∩C)=25, n(M∩P∩C)=10. Total = 120. Using inclusion-exclusion: n(M∪P∪C) = 70+60+50 - (30+28+25) + 10 = 180 - 83 + 10 = 107. So number who like at least one = 107. Those who dislike all three = 120 - 107 = 13.
Hint
Use n(A∪B∪C) = n(A)+n(B)+n(C) - n(A∩B)-n(A∩C)-n(B∩C) + n(A∩B∩C).