From 50 students taking examination in mathematics physics and chemistry

Asked by admin @ 06/08/2021 in Math viewed by 342 People

From 50 students taking examination in mathematics, physics and chemistry , 37 passed maths ,24 physics and 43 chemistry .Atmost 19 passed maths and physics ,atmost 29 passed maths and chemistry and atmost 20 passed physics and chemistry .The largest possible no. that could have passed all three examination is

a -11. b-12. c-13. d-14.

Answered by admin @ 06/08/2021

Answer:

The answer is 14.

Steps:

Given,

n(M∪P∪C) = 50

n(M) = 57

n(P) = 24

n(C) = 43

n(M∩P) ≤ 19

n(M∩C) ≤ 29

n(P∩C) ≤ 20

Let n(M∩P∩C) = x

We know that

n(M∪P∪C) = n(M) + n(P) + n(C) - n(M∩P) - n(P∩C) - n(M∩C) - n(M∩P∩C)

⇒ n(M∪P∪C) ≤ n(M) + n(P) + n(C) - n(M∩P) - n(P∩C) - n(M∩C) - n(M∩P∩C)

⇒ 50 ≤ 37 + 24 + 43 - 19 - 20 - 29 - x

⇒ 50 ≤ 104 - 68 + x

⇒ 50 ≤ 36 + x

⇒ 50 - 36 ≤ x

⇒ 14 ≤ x

⇒ x ≥ 14

Regarding to that, we can say that the largest possible number that that could have passed in 3 subjects is 14.

PS: Please look at the attachment to understand better.

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