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  • In a class 82 people were asked their favourite fruits?39 people likes apples,50 likes banana,39 like pears,21 liked apple and bananas,28 liked banana and pears,19 liked apple and pears.How many liked all type of three fruits??

In a class 82 people were asked their favourite fruits?39 people likes apples,50 likes banana,39 like pears,21 liked apple and bananas,28 liked banana and pears,19 liked apple and pears.How many liked all type of three fruits??

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Solution: Let A , B and C denote set of student who Apples , bananas and pears respectively

Then, n(A)=39;n(B)=50;n(C)=39;n(Acap B)=21;n(Bcap C)=18;n(Acap C)=19\ \Rightarrow n(Acup Bcup C)=n(A)+n(B)+n(C)-n(Acap B)-n(Bcap C)-n(Acap C)+n(Acap Bcap C)\ \Rightarrow 82=39+50+39-21-18-19+n(Acap Bcap C)\ \Rightarrow n(Acap Bcap C)=12

12 people like three type of fruits

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Deependra Verma

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