Question

Out of 200 students; 35 students failed in MHT-CET, 40 in AIEEE and 40 in IIT entrance, 20 failed in MHT-CET and AIEEE, 17 in AIEEE and IIT entrance, 15 in MHT-CET and IIT entrance, and 5 failed in all three examinations. Find how many students: failed in AIEEE or IIT entrance.

Answer 1

Let A = Set of students who failed in MHT-CET

B = Set of students who failed in AIEEE

C = Set of students who failed in IIT entrance

X = Set of all students

∴ n(X) = 200, n(A) = 35, n(B) = 40, n(C) = 40,

n(A ∩ B) = 20, n(B ∩ C) = 17, n(A ∩ C) = 15, n(A ∩ B ∩ C) = 5

No. of students who failed in AIEEE or IIT entrance

= n(B ∪ C)

= n(B) + n(C) – n(B ∩ C)

= 40 + 40 – 17

= 63