Question Detail
Question
In a survey of 120 students in the Faculty of Physical and Earth Sciences, 70 Students like Mathematics, 60 Students like Physics and 50 Students like Chemistry. If 30 students offer Mathematics and Physics, 20 offer Mathematics and Chemistry and 25 Students like Physics and Chemistry. Now, suppose 15 like the three Subjects, how many dislike the three Subjects?
Correct Answer
Option B is the correct answer.
Detailed Explanation
n(M∪P∪C) = n(M)+n(P)+n(C) - n(M∩P) - n(M∩C) - n(P∩C) + n(M∩P∩C) = 70+60+50 - 30 - 20 - 25 + 15 = 180 - 75 + 15 = 120. So all 120 like at least one, so number who dislike all three = 0.
Hint
Use inclusion-exclusion principle for three sets.