Find How Many Drink Tea and Coffee
Question:
In a group of 50 persons, 14 drink tea but not coffee and 30 drink tea. Find:
(i) how many drink tea and coffee both
(ii) how many drink coffee but not tea.
Solution
(i)
\[ n(T)=n(T-C)+n(T\cap C) \] \[ 30=14+n(T\cap C) \] \[ n(T\cap C)=16 \](ii)
\[ 50=14+16+n(C-T) \] \[ 50=30+n(C-T) \] \[ n(C-T)=20 \]Hence,
\[ \boxed{n(T\cap C)=16} \] \[ \boxed{n(C-T)=20} \]