Q. 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
Explanation
(a)
Given, $n(N) = 12,\ n(P) = 16,\ n(H) = 18$,
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ n(N \cup P \cup H) = 30$
And $n(N \cap P \cap H) = 0$
Now, $n(N \cup P \cup H) = n(N) + n(P) + n(H)$
$- n(N \cap P) - n(P \cap H) - n(H \cap N)$
$+ n(N \cap P \cap H)$
$\Rightarrow n(N \cap P) + n(P \cap H) + n(H \cap N) = (12 + 16 + 18) - 30$
$= 46 - 30 = 16$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.