In a group of 100 persons, liking at least one of tea, coffee, ice-
cream, 49 like tea, 41 like coffee, 62 like ice-cream. 25 persons like tea and coffee both, 18 persons like coffee and ice-cream both and 17 persons like both tea and ice-cream. Find the number of persons who like all the three items.
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Let T,C, and I denote the set of persons who like tea,coffee and ice-cream respectiively.Then,nU=100,nT=49,nC=41,nI=62,nTC=25,nCI=18,nTI=17,Required number of persons=nU-nT-nC-nI+nTC+nCI+nTI=100-49-41-62+25+18+17=8

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