According to the question,
Total number of students = 100
Number of students who passed in English = 15
Number of students who passed in Mathematics = 12
Number of students who passed in Science = 8
Number of students who passed in English and Mathematics = 6
Number of students who passed in Mathematics and Science = 7
Number of students who passed in English and Science = 4
Number of students who passed in all three = 4
Let the total number of students = U
Let the number of students passed in English = E
Let the number of students passed in Mathematics = M
Let the number of students passed in Science = S
n(M ∩ S ∩ E) = a = 4
n(M ∩ S) = a + d = 7
⇒ 4 + d = 7
⇒ d = 3
n(M ∩ E) = a + b = 6
⇒ 4 + b = 6
⇒ b = 2
n(S ∩ E) = a + c = 4
⇒ 4 + c = 4
⇒ c = 0
n(M) = e + d + a + b = 12
⇒ e + 4 + 3 + 2 = 12
⇒ e + 9 = 12
⇒ e = 3
n(E) = g + c + a + b = 15
⇒ g + 0 + 4 + 2 = 15
⇒ g + 6 = 15
⇒ g = 9
n(S) = f + c + a + d = 8
⇒ f + 0 + 4 + 3 = 8
⇒ f + 7 = 8
⇒ f = 1
Therefore, from the above equations, we get that,
(i) Number of students passed in English and Mathematics but not in Science = b = 2
(ii) Number of students in Mathematics and Science but not in English = d = 3
(iii) Number of students in Mathematics only = e = 3
(iv) Number of students in more than one subject only = a + b + c + d = 4 + 3 + 2 + 0 = 9