Question

In a certain group of 36 people, 18 are wearing hats and 24 are wearing sweaters. If six people are wearing neither a hat nor a sweater, then how many people are wearing both a hat and a sweater ?

• A. $30$
• B. $22$
• C. $12$
• D. $8$

Answer 1

Answer: (C)

$12$

Since 6 people are wearing neither hat nor sweater

$n(H\cup S)=36-6=30$

By set theory

$n(H\cap S)=n\left(H\right)+n\left(S\right)-n(H\cup S)$

$=18+24-30=12$