Question
In a group of 100 students, 70 like tea, 60 like coffee,
and 50 like juice. 35 like both tea and coffee, 32 like both tea and juice, and 25 like both coffee and juice. 8 students like all three drinks. How many students like none of the three drinks?Solution
ATQ, Let sets T, C, J represent tea, coffee, juice. By inclusion–exclusion: |T ∪ C ∪ J| = |T| + |C| + |J| − |T∩C| − |T∩J| − |C∩J| + |T∩C∩J| = 70 + 60 + 50 − 35 − 32 − 25 + 8 = 180 − 92 + 8 = 96. So 96 students like at least one of the three. Therefore, students who like none = 100 − 96 = 4.
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