Question

Out of a total of $800$ boys in a school, $224$ play cricket, $240$ play hockey, and $336$ play basketball. Out of the total, $64$ play both basketball and hockey, $80$ play cricket and basketball, and $40$ play cricket and hockey, $24$ play all the three games. The number of boys who did not play any game is:

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

Answer 1

The correct option is A $160$

Total no. of boys $n\left(X\right)=800$
Let $n\left(C\right)=$ Boys who played cricket
$n\left(H\right)=$ Boys who played hockey
$n\left(B\right)=$ Boys who played basketball
$\therefore n\left(C\right)=224,n\left(H\right)=240,n\left(B\right)=336,n(B\cap H)=64,n(C\cap B)=80,n(C\cap H)=40,n(C\cap H\cap B)=24$
$\therefore n(C\cup H\cup B)=n\left(C\right)+n\left(H\right)+n\left(B\right)-n(B\cap H)-n(C\cap B)-n(B\cap H)+n(C\cap H\cap B)$
$\Rightarrow 224+240+336-64-80-40+24=640$
The number of boys who did not play any game $=n\left(X\right)-n(C\cup H\cup B)\Rightarrow 800-640=160$