Question
In a survey of 200 people: 112 like coffee (C), 125 like
tea (T), 90 like juice (J). 60 like both C and T, 55 like T and J, 52 like C and J. If 30 like all three, how many like exactly one drink?Solution
ATQ,
Use inclusion: |C∪T∪J| = 112 + 125 + 90 − 60 − 55 − 52 + 30 = 190. Let only C = 112 − 60 − 52 + 30 = 30. Only T = 125 − 60 − 55 + 30 = 40. Only J = 90 − 55 − 52 + 30 = 13. Exactly one = 30 + 40 + 13 = 83.
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