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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 those 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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E
67
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Solution

## The correct option is B 28Here, n(C)=40, n(F)=16, n(H)=11, n(C∩F)=8, n(C∩H)=6, n(F∩H)=2, n(C∩F∩H)=1⇒n(C∪F∪H)=40+16+11−8−6−2+1=52⇒n(C′∩F′∩H′) =n(U)−n(C∪F∪H) =80−52=28

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