Club A has 20 members and club B has 27. If a total of 42 people belong to two clubs, how many people belong to both clubs?

Question: Club A has 20 members and club B has 27. If a total of 42 people belong to two clubs, how many people belong to both clubs?

Solution:
Given that,
Members in Club A = 20
Members in Club B = 27
Total distinct members = 42

We know,
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
⇒ 42 = 20 + 27 - n(A ∩ B)
⇒ 42 = 47 - n(A ∩ B)
⇒ n(A ∩ B) = 47 - 42
∴ n(A ∩ B) = 5