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Out of 800 boys in a school, 224 played Cricket, 240 played Hockey and 336 played Basketball. Of the total, 64 played both Basketball and Hockey; 80 played Cricket and Basketball and 40 played Cricket and Hockey; 24 played all the three games. The number of boys who did not play any game is 

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Detailed Solution

 Here, n(C)=224,n(H)=240,n(B)=336 , n(H∩B)=64,n(B∩C)=80,n(H∩C)=40 , n(C∩H∩B)=24

∴nCc∩Hc∩Bc=n(C∪H∪B)c=n(U)−n(C∪H∪B)=800−[224+240+336−64−80−40+24]=800−640=160

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Out of 800 boys in a school, 224 played Cricket, 240 played Hockey and 336 played Basketball. Of the total, 64 played both Basketball and Hockey; 80 played Cricket and Basketball and 40 played Cricket and Hockey; 24 played all the three games. The number of boys who did not play any game is