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Byju's Answer

Standard XIII

Mathematics

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

In a class, t...

Question

In a class, there are $200$ students in which $120$ take Mathematics, $90$ take Physics, $60$ take Chemistry, $50$ take Mathematics and Physics, $50$ take Mathematics and Chemistry, $43$ take Physics and Chemistry and $38$ take Mathematics, Physics and Chemistry. Then the number of students who have taken exactly one subject is

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Solution

Let $M, P, C$ denote the set of students who have taken Mathematics, Physics and Chemistry respectively.
$n (M) = 120, n (P) = 90, n (C) = 60$
$n (M \cap P) = 50, n (M \cap C) = 50, n (P \cap C) = 43, n (M \cap P \cap C) = 38$
$∴$ Number of students taking exactly one subject
$= n (M) + n (P) + n (C)$
$- 2 n (M \cap P) - 2 n (P \cap C) - 2 n (M \cap C) + 3 n (M \cap P \cap C)$
$= 120 + 90 + 60 - 2 (50) - 2 (43) - 2 (50) + 3 (38)$
$= 98$

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