Correct Answer - Option 3 : A
Given:
Total student = 3200
Numbers of student know English, n(E) = 2400
Numbers of student know Telugu, n(T) = 1700
Numbers of student know Hindi, n(H) = 800
Numbers of student know both English and Telugu, n(E ∩ T) = 1000
Numbers of student know both English and Hindi, n(H ∩ E) = 500
Numbers of student know both Hindi and Telugu, n(H ∩ T) = 300
Numbers of student know all three languages, n(E ∩ H ∩ T) = 100
Formula used:
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C)
Where,
(A ∪ B) → Total A and B
(A) → Total A
(B) → Total B
(C) → Total C
(A ∩ B) → Total common part of A and B
(A ∩ C) → Total common part of A and C
(C ∩ B) → Total common part of C and B
(A ∩ B ∩ C) → Total common part of A, B and C.
Calculation:
Numbers of student know all three language = n(E) + n(T) + n(H) − n(E ∩ T) − n(H ∩ E) − n(H ∩ T) + n(E ∩ T ∩ H)
⇒ n(E ∪ T ∪ H) = 2400 + 1700 + 800 − 1000 − 500 − 300 + 100
⇒ 3200
Number of student do not know any of the three languages = 3200 − 3200 = 0
∴ Number of student do not know any of the three languages is 0.