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

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

  1. A

    128

  2. B

    216

  3. C

    240

  4. D

    160

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    Solution:

    Given n(C)=224,n(H)=240,n(B)=336,n(HB)=64,n(BC)=80,n(HC)=40n(CHB)=24

    We know that n(CCHCBC)=n[(CHB)C]=n(U)n(CHB)

    Substitute the appropriate values in the above equation

    n(CCHCBC)=800n(C)+n(H)+n(B)n(HC)n(HB)n(CB)+n(CHB) =800[224+240+336648040+24] =800-[824184] =984824 =160

    Therefore, n(CCHCBC)=160

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