In a class of $$30$$ pupils, $$12$$ take needle 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

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Infinity Learn · Accepted Answer

Given $$n(N)=12$$, $$n(P)=16$$, $$n(H)=18$$, $$n(N$$∪P∪$$H)=30From$$, $$n(N$$∪P∪$$H)=n(N)+n(P)+n(H)-n(N$$∩$$P)-n(P$$∩$$H)-n(N$$∩$$H)+n(N$$∩P∩$$H)$$∴$$n(N$$∩$$P)+n(P$$∩$$H)+n(N$$∩$$H)=16Now$$, number of pupils taking two $$subjects=n(N$$∩$$P)+n(P$$∩$$H)+n(N$$∩$$H)-3n(N$$∩P∩$$H)=16-0=16$$.

In a class of 30 pupils, 12 take needle 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

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