Question

In group of $40$ students, $26$ take tea, $18$ take coffee and $8$ take neither of the two. How many take both tea and Coffee?

Answer 1

Let $n\left(S\right)=$ Number of students.

$n\left(T\right)=$ Number of students who take tea.

$n\left(C\right)=$ Number of students who take coffee.

$n\left(D\right)=$ Student who take neither tea nor coffee.

$n\left(S\right)=40;n\left(T\right)=26;n\left(C\right)=18;n\left(D\right)=8$

$n(T\cup C)=n\left(S\right)-n\left(D\right)$

$=40-8$

$n(T\cup C)=32$

Student who take both coffee and tea = $T\cap C$

$n(T\cap C)=n\left(T\right)+n\left(C\right)-n(T\cup C)$

$=26+18-32$

$n(T\cup C)=12$

Number of students who take both tea and coffee $=12$.