Question

In a group of students in a class, 20 are in the debating club, 24 in the drama club and 27 in the recitation club. If 12 like drama and debate, 10 like recitation and debate, 14 like drama and recitation and 7 like all the three activities, then the total number of students in the class is

Options

• 40

• 42

• 50

• 52

Answer 1

42

Explanation:

Number of students like debating, n(A) = 20

Number of students like drama, n(B) = 24

Number of students like recitation, n(C) = 27

Number of students like debating and drama, n (A ∩ B) = 12

Number of students like debating and recitation, n (A ∩ C) = 10

Number of students like recitation and drama, n (B ∩ C) = 14

Number of students like All the three n (A ∩ B ∩ C) = 7

∴ Number of the student in the class
n (A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(C ∩ A) + n (A ∩ B ∩ C)

∴ n (A ∪ B ∪ C) = 20 + 24 + 27 − 12 − 10 − 14 + 7= 42