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Question

In a class of 80 students numbered 1 to 80, all odd numbered students opt for cricket, students whose numbers are divisible by 5 opt for football and students whose numbers are divisible by 7 opt for hockey. The number of students who do not opt any of the three games, is -

A
13
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B
24
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C
28
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D
52
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Solution

The correct option is C 28
Set of students who opt Cricket = A
Set of students who opt Football = B
Set of students who opt Hockey = C

From the given information,
n(A)=40,n(B)=16,n(C)=11
n(AB)=8, n(AC)=6, n(BC)=2
n(ABC)=1

Using n(ABC)=n(A)+n(B)+n(C)n(AB)n(BC)n(CA)+n(ABC)
=40+16+11862+1=52

And the number of students who do not opt any of the three games are given by n(AcBcCc)=n(U)n(ABC)=8052=28

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n(A∪B∪C) = n(A) + n(B) + n(C) − n(A∩B) − n(B∩C) − n(C∩A) + n(A∩B∩C)
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