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 :

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 :

1 Answer

127 votes

Let n(A) = number of students opted Mathematics = 70,

n(B) = number of students opted Physics = 46,

n(C) = number of students opted Chemistry = 28,

n(A ∩ B) = 23,

n(B ∩ C) = 9,

n(A ∩ C) = 14,

n(A ∩ B ∩ C) = 4,

Now n(A B C)

= n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) n(A ∩ C) + n(A ∩ B ∩ C)

= 70 + 46 + 28 23 − 9 − 14 + 4 = 102

So number of students not opted for any course

= Total − n(A B C)

= 140 − 102 = 38

127 votes

127