Question

A group of $123$ workers went to a canteen for cold drinks, ice-cream and tea. $42$ workers took ice-cream, $36$ took tea and $30$ took cold drinks. $15$ workers purchased ice-cream and tea, $10$ purchased ice-cream and cold drinks, and $4$ purchased cold drinks and tea but not ice-cream. Then the number of workers who did not purchase anything is

Answer 1

$n\left(U\right)=123$
$n\left(I\right)=42,n\left(T\right)=36,n\left(C\right)=30$
$n(I\cap T)=15,n(I\cap C)=10$
$n(C\cap T\cap I^{\prime })=4$
$n(C\cap T\cap I^{\prime })=4=n(C\cap T)-n(C\cap T\cap I)$

Number of workers who did not purchase anything $=n(C\cup T\cup I{)}^{\prime }$
$=n\left(U\right)-n(C\cup T\cup I)=123-[42+36+30-15-10-4]=44$