Question

Q.3 In a board examination, 40 students failed in physics, 40 in chemistry and 35 in
mathematics, 20 failed in maths and physics, 17 in physics and chemistry, 15 in maths and
chemistry and 5 in all three subjects. If 350 students appeared in the examination, how
many of them did not fail in any subject?

Answer 1

Answer:

The answer is 282 students.

Answer 2

The number of students who didn't fail in any of the subjects is 282.

Given,

n(X) = 350.

n(P) = 40, n(C) = 40, n(M) = 35.

n(PnM) =20, n(PnC) = 17, n(MnC) = 15

n(PnMnC) = 5

To Find,

The number of students who didn't fail in any of the subjects.

Solution,

Let's find the number of students who failed in at least one of the subjects.

n(PuCuM) = n(P) + n(C) + n(M) - n(PnM)- n(MnC)-n(PnC)+n(PnMnC)
n(PuCuM) = 40 +40+25-17-20-15+5

n(PuCuM) = 68.

Let's find the number of students who didn't fail in any of the subjects.

= n(X) - n(PuCuM)

= 350 - 68

= 282.

The number of students who didn't fail in any of the subjects is 282.

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