Question

In a certain group of 36 people, only 18 are wearing hats and only 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?

Answer 1

Number of people wearing a hat or a sweater or both = 36 – 6 = 30 

n ( H ∪ S) = n (H) + n (S) – n (H ∩ S)

30 = 18 + 24 – n (H ∩ S) 

⇒ n (H ∩ S) + 42 – 30 = 12.