1.Set Theory
medium

In a class of $30$ pupils, $12$ take needle work, $16$ take physics and $18$ take history. If all the $30$ students take at least one subject and no one takes all three then the number of pupils taking $2$ subjects is

A

$16$

B

$6$

C

$8$

D

$20$

Solution

(a) Given $n(N) = 12$, $n(P) = 16$, $n(H) = 18$, $n(N \cup P \cup H) = 30$

From, $n(N \cup P \cup H) = n(N) + n(P) + n(H) – n(N \cap P)$

$ – n(P \cap H) – n(N \cap H) + n(N \cap P \cap H)$

 $\therefore n(N \cap P) + n(P \cap H) + n(N \cap H) = 16$

Now, number of pupils taking two subjects

$ = n(N \cap P) + n(P \cap H) + n(N \cap H) – 3n(N \cap P \cap H)$

$ = 16 – 0 = 16$.

Standard 11
Mathematics

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