Question

In a class of $30$ pupils. $12$ take needls 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

Answer 1

Answer: (A)

Given that $n(N)=12,n(P)=16,n(H)=18,$
$n(N\cup P\cup H)=30$
and $n(N\cap P\cap H)=0$
Now, $n(N\cup P\cup H)=n(N)+n(P)+n(H)$
$-n(N\cup P)-n(P\cap H)-n(H\cap N)$
$+n(N\cap P\cap H)$
$\Rightarrow$ $n(N\cap P)+N(P\cap H)+N(H\cap N)$
$=n(N)+n(P)+n(H)-n(N\cup P\cup H)$
$=(12+16+18)-30$
$=46-30=16$