Question

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

• A. 128
• B. 216
• C. 240
• D. 160

Answer 1

Answer: (D)

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