Question

In a class of $100$ students, $60$ like mathematics, $72$ like physics, $68$ like chemistry and no student likes all three subjects. Then number of students who don't like mathematics and chemistry is

Answer 1

$100=60+72+68-(x+y+z)+0x+y+z=100$
So no student like only maths, or only physics or only chemistry
So $\begin{array}{c}x+y=60\\ x+z=72\\ y+z=68\end{array}\}\Rightarrow y=28$
Now $n(M^{\prime }\cap C^{\prime })=100-n(M\cup C)$
$=100-(60+68-y)=y-28=0$