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Question
In a class of 200 students who appeared in certain examinations, 35 students failed in CET, 40 in NEET and 40 in JEE, 20 failed in CET and NEET, 17 in NEET and JEE, 15 in CET and JEE, and 5 failed in all three examinations. Find how many students, did not fail in any examination.
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Solution
Let A = set of students who failed in CET
B = set of students who failed in NEET
C = set of students who failed in JEE
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 and n(A ∩ B ∩ C) n = 5
n(A ∪ B ∪ C)
= n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C)
= 35 + 40 + 40 − 20 − 17 − 15 + 5
= 68
∴ No. of students who did not fail in any exam
= n(X) − n(A ∪ B ∪ C)
= 200 − 68
= 132
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