Question

. In a survey of 200 students of a school, it was found that 120 study Mathematics,90 study Physics and 70 study Chemistry,40 study Mathematics and Physics,30 study Physics and Chemistry,50 study Chemistry and Mathematics and 20 none of these. Find the number of students who study (i) all the three (ii) Mathematics or Physics but not Chemistry (iii) Mathematics and Physic, but not Chemistry (iv) Mathematic and Chemistry, but not Physics (v) only Mathematics (vi) Physics and Chemistry but not Mathematics

Answer 1

M = Mathematics ; P = Physics and C = Chemistry 

n(M) = 120 n(P) = 90 n (C) = 70 n ( M ∩ P) = 40 

n ( P ∩ C ) = 30 n ( C ∩ M ) = 50 n ( M ∪ P ∪ C )’ = 20 

Now n(M ∪ P ∪ C)’ = n(U) – n(M ∪ P ∪ C) 

20 = 200 – n (M ∪ P ∪ C) 

Therefore, n(M ∪ P ∪ C) = 200 – 20 = 180 

n(M ∪ P ∪ C) 

= n(M) + n(P) + n(C) – n(M ∩ P) – n(P ∩ C) – n(C ∩ M) + n(M ∩ P ∩ C)

180 = 120 + 90 + 70 - 40 - 30 - 50 + n(M ∩ P ∩ C)

⇒ n(M ∩ P ∩ C) =180 - 120 - 90 - 70 + 40 + 30 + 50 

⇒ n(M ∩ P ∩ C) = 20.

Answer 2

Explanation:

a survey of 200 students of a school, it was found that 120 study Mathematics, 90 study Physics and 70 study Chemistry, 40 study Mathematics and Physics, 30 study Physics and Chemistry, 50 study Chemistry and Mathematics and 20 none of these subjects. Find the number of students who study all the three subjects.

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