Question

Out of $800$ boys in 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

• A. $160$
• B. $240$
• C. $216$
• D. $128$

Answer 1

The correct option is A $160$

$n\left(C\right)=224,n\left(H\right)=240,n\left(B\right)=336,n(H\cap B)=64,n(B\cap C)=80,n(H\cap C)=0,n(C\cap H\cap B)=24$
$n(C^{\prime }\cap H^{\prime }\cap B^{\prime })=n{(C\cup H\cup B)}^{\prime }=n\left(U\right)-n(C\cup H\cup B)=800-[n\left(C\right)+n\left(H\right)+n\left(B\right)-n(H\cap C)-n(H\cap B)-n(C\cap B)+n(C\cap H\cap B)]=800-[224+240+336-64-80-40+24]=800-[824-184]=984-824=160$