Question

In a class of $50$ students $35$ opted for Mathematics and $37$ opted for Biology How may have opted for only Mathematics? ( Assume that each student has to opt for at least one of the subjects)

• A. $15$
• B. $17$
• C. $13$
• D. $19$

Answer 1

Answer: (C)

$13$

Here $n$$(M\cup B)$ $=50$, $n\left(M\right)=35$, $n\left(B\right)=37$
$\therefore n(M\cap B)=n\left(M\right)+n\left(B\right)-n(M\cup B)$
$=35+37-50=22$
$\Rightarrow$ $22$ student have opted for both Mathematics and Biology.

Now the number of students who have opted for Mathematics only
$=n\left(M\right)-n$$(M\cap B)$
$=35-22=13$