Find How Many Like Both Coffee and Tea
Question:
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?
Solution
\[ n(C\cup T)=n(C)+n(T)-n(C\cap T) \] \[ 70=37+52-n(C\cap T) \] \[ 70=89-n(C\cap T) \] \[ n(C\cap T)=89-70 \] \[ n(C\cap T)=19 \]Hence, 19 people like both coffee and tea.