Discussion
In a class of 120 students, 90 students passed in History, 65 students passed in Sociology and 30 students failed in both the subjects. How many students passed in both the subjects?
Answer: C
Total students = 120.
Number of students who failed in both subjects = 30.
Number of students who passed in at least one subject = Total students - Failed in both = 120 - 30 = 90.
So, n(H ∪ S) = 90.
Given n(H) = 90 and n(S) = 65.
Using the formula n(H ∪ S) = n(H) + n(S) - n(H ∩ S):
90 = 90 + 65 - n(H ∩ S)
n(H ∩ S) = 155 - 90 = 65.
So, 65 students passed in both subjects.
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