Question

A group of $123$ workers went to a canteen for coffee, ice-cream and tea. $42$ workers took ice-cream, $36$ took tea and $30$ took coffee. $15$ workers purchased ice cream and tea, $10$ ice cream and coffee and $4$ coffee and tea but not ice cream, while $11$ took ice cream and tea but not coffee. Determine how many workers did not purchase anything ?

Answer 1

From the figure, we have

$n(I\cap C\cap T)=15-11=4$

$n(C\cap T)=n\left(\right(C\cap T)\cap I^{\prime })+n(C\cap T\cap I)=4+4=8$

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

$=30+42+36-15-8-10+4$

$=79$

So, the number of workers who did not purchase anything $=$ $123-79=44$.