Question

In a school, 80 students like Maths, 90 students like Science, 82 students like History, 21 like both Maths and Science, 19 like both Science and History 20 like both Maths and History and 8 liked all the three subjects. If each student like atleast one subject, then find 

(i) the number of students in the school 

(ii) the number of students who like only one subject.

Answer 1

Let M, S and H represent sets of students who like Maths, Science and History respectively. 

Then, n(M) = 80, n(S) = 90, n(H) = 82, n(M ∩ S) = 21, n(S ∩ H) = 19, n(M ∩ H) = 20, n(M ∩ S ∩ H) = 8 

Let us represents the given data in a venn diagram.

(i) The number of student in the school = 52 + 59 + 55 + 12 + 11 + 8 + 8 = 205 

(ii) The number of students who like only one subject = 52 + 59 + 55 

= 166