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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    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                                      [DCE 1995; MP PET 1996]

    A) 128

    B) 216

    C) 240

    D) 160

    Correct Answer: D

    Solution :

    \[n\,(C)=224,\,n\,(H)=240,n\,(B)=336\] \[n\,(H\cap B)=64,\,\,n(B\cap C)=80\] \[n(H\cap C)=40\], \[n(C\cap H\cap B)=24\] \[n\,({{C}^{c}}\cap {{H}^{c}}\cap {{B}^{C}})=n\,[{{(C\cup H\cup B)}^{c}}]\] \[=n(\cup )-n(C\cup H\cup B)\] \[=800-[n(C)+n(H)+n(B)-n(H\cap C)\] \[-n(H\cap B)-n(C\cap B)+n(C\cap H\cap B)]\] \[=800-[224+240+336-64-80-40+24]\] \[=800-640=160\].


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