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Question

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
6
8
20

The correct answer is: (a) 16

Given, $n open parentheses N close parentheses equals 12 comma blank n open parentheses P close parentheses equals 16 comma blank n open parentheses H close parentheses equals 18$ ,
$n open parentheses N union P union H close parentheses equals 30$
And $n open parentheses N intersection P intersection H close parentheses equals 0$
Now, $n open parentheses N union P union H close parentheses equals n open parentheses N close parentheses plus n open parentheses P close parentheses plus n open parentheses H close parentheses$
$negative n open parentheses N intersection P close parentheses minus n open parentheses P intersection H close parentheses minus n open parentheses H intersection N close parentheses$
$plus n left parenthesis N intersection P intersection H right parenthesis$
$rightwards double arrow n open parentheses N intersection P close parentheses plus n open parentheses P intersection H close parentheses plus n open parentheses H intersection N close parentheses equals open parentheses 12 plus 16 plus 18 close parentheses minus 30$
$equals 46 minus 30 equals 16$

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