How many students in this group are not taking any of the three subjects?

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Solution

The correct option is D 9
7 students are taking Physics only.

So

$7 = n (P) - n (P \cap G) - n (P \cap E) + n (P \cap G \cap E)$

$\Rightarrow n (P) = 7$ $+ n (P \cap G) + n (P \cap E) - n (P \cap G \cap E)$

So $n (P) = 7 + 24 + 30 - 16 = 45$

Similarly $n (G) = 10 + 24 + 22 - 16 = 40$

$n (E) = 5 + 22 + 30 - 16 = 41$

$n (P \cup G \cup E) = n (P) + n (G) + n (E)$ $- n (G \cap E) - n (P \cap G) - n (P \cap E) + n (P \cap G \cap E)$

$= 45 + 40 + 41 - 22 - 24 - 30 + 16 = 66$

$75 - 66 = 9$ students are not taking any of the 3 subjects.

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