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\left(C\right)=224,n\left(H\right)=240,n\left(B\right)=336,n\left(H\cap B\right)=64,n\left(B\cap C\right)=80,n\left(H\cap C\right)=40$$n\left(C\cap H\cap B\right)=24$

We know that $n\left({C}^{C}\cap {H}^{C}\cap {B}^{C}\right)=n\left[{\left(C\cup H\cup B\right)}^{C}\right]=n\left(U\right)-n\left(C\cup H\cup B\right)$

Substitute the appropriate values in the above equation

Therefore, $\begin{array}{rcl}n\left({C}^{C}\cap {H}^{C}\cap {B}^{C}\right)& =& \overline{)160}\end{array}$  Register to Get Free Mock Test and Study Material

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