In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is

Answers (1)

We know,

\\ n (A \cup B \cup C) = n (A) + n (B) + n (C) - n (A \cap B) - n (A \cap C) - n (B \cap C) + n (A \cap B \cap C)

According to question.

Let no. of students opted maths = n(A)  = 70

student opted physics = n(B) = 40

student opted chemistry = n(C) = 28

n\left (A\cap B \right ) = 23 , n\left (A\cap C \right ) = 14 , n\left (B\cap C \right ) = 9

n\left (A\cap B \cap C \right ) = 4

\\ Now , n\left (A\cap B \cap C \right ) = n(A) + n(B) + n(C) - n\left ( A\cap B \right ) - n\left ( A\cap c \right ) - n\left ( B\cap C \right ) + n\left (A\cap B \cap C \right ) = 70 + 40 + 28 - 23 - 14 + 4 = 102

Therefore, total no. of student not adopting any course = total - n\left (A\cap B \cap C \right ) = 140 - 102 = 38

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