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Question

A group of 123 workers went to a canteen for cold drinks, ice-cream and tea. 42 workers took ice-cream, 36 took tea and 30 took cold drinks. 15 workers purchased ice-cream and tea, 10 purchased ice-cream and cold drinks, and 4 purchased cold drinks and tea but not ice-cream. Then how many workers did not purchase anything ?

A
44
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B
46
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C
48
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D
42
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Solution

The correct option is A 44
n(U)=123
n(I)=42, n(T)=36, n(C)=30
n(IT)=15, n(IC)=10
n(CTI)=4
n(CTI)=4=n(CT)n(CTI)

Number of workers who did not purchase anything =n(CTI)
=n(U)n(CTI)=123[42+36+3015104]=44

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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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