• # question_answer In a class of 30 pupils, 12 take needle work 16 take Physics and 18 take History. If all the30 students take at least one subject and no one take all three, then the number of pupils taking 2 subjects is A)  16                               B)  6                 C)  8                                 D)  20

Given, $n(N)=12,\,\,n(P)=16,\,\,n(H)=18$ and      $n(N\cup P\cup H)=30$ $\because$ $n(N\cup P\cup H)=n(N)+n(P)+n(H)$ $-n(N\cap P)$ s$-n(N\cap H)-n(N\cap H)+n(N\cap P\cap H)$ $\Rightarrow$ $30=12+16+18-n(N\cap P)-n(P\cap H)$ $-n(N\cap H)+0$ $\Rightarrow$ $n(N\cap P)+n(P\cap H)+n(N\cap H)=16$ $\therefore$ Number of pupils taking two subjects $=\,n(N\cap P)+n(P\cap H)+n(N\cap H)$ $-3n(N\cap P\cap H)$ $=16-0=16$