Question

In a group of $15$ women, $7$ have nose studs, $8$ have ear rings and $3$ have neither. How many of these have both nose studs and ear rings?

• A. $0$
• B. $2$
• C. $3$
• D. $7$

Answer 1

The correct option is C $3$

let A ,B,C be the women who have ear rings,nose studs and wear neither ring nor nose studs.

Total number of students=15

$n(A\cup B)=15-n\left(C\right)$

$n(A\cup B)=15-3$

$n(A\cup B)=12$

$n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$

$=8+7-12=15-12=3$

So the number of students who have bothstuds and rings equal to 3.