In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many like both coffee and tea?
A total number of people = 70.
Number of people liking Coffee = n(C) = 37.
Number of people liking Tea = n(T) = 52
Total number = n (C ∪ T) = 70
Person who likes both would be n(C ∩ T)
We know,
n (C ∪ T) = n(C) + n(T) – n (C ∩ T)
Substituting the values we get
70 = 37+52– n (C ∩ T)
70 = 89 – n (C ∩ T)
n (C ∩ T) =19.
∴ There are 19 persons who like both coffee and tea.