Question

In a college, $60$ students enrolled in chemistry, $40$ in physics, $30$ in biology, $15$ in chemistry and physics, $10$ in physics and biology, $5$ in biology and chemistry. No one enrolled in all the three. Find how many are enrolled in at least one of the subjects.

Answer 1

We are given $n\left(C\right)=60$ , $n\left(P\right)=40$ and $n\left(B\right)=30$

$n(C\cap P)=15$ , $n(P\cap B)=10$ , $n(B\cap C)=5$

Since $n(C\cap P\cap B)=0$

The required answer is $n(C\cup P\cup B\cup )$

$n(C\cup P\cup B\cup )=n\left(C\right)+n\left(P\right)+n\left(B\right)-n(C\cap P)-n(P\cap B)-n(B\cap C)+n(C\cap B\cap P)$

$\Rightarrow n(C\cup P\cup B\cup )$

$=60+40+30-15-10-5=100$