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Question

In a class of 30 pupils, 12 take Chemistry, 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

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B

6

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C

8

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D

20

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Solution

The correct option is A

16


Explanation for the correct option:

Finding the number of pupils taking 2 subject:

Total number of people in class=30

Number of people who take Chemistry, n(C) =12

Number of people who take Physic, n(P)=16

Number of people who take History,n(H)=18

Also given,

n(CPH)=30,n(CPH)=0

Now, as we know,

(CPH)=n(C)+n(P)+n(H)n(CP)n(PH)n(HC)+n(CPH)+n(CP)+n(PH)+n(HC)

(CPH)=12+16+18n(CP)n(PH)n(HC)+0

n(CP)+n(PH)+n(HC)=(12+16+18)30=4630=16

Hence, the correct option is A.


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