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Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basket ball, of the total 64 played both basket ball and hockey, 80 played cricket and basketball and 40 played cricket and hockey, 24 played all these three games. The numbers of boys who did not play any game is:
A) 128
B) 216
C) 240
D) 160
Correct answer:
D) 160
Description for Correct answer:
We have \( \Large n \left(c\right)=224,\ n \left(H\right)=240,\ n \left(B\right)=336 \)
\( \Large n \left(H \cap B\right)=64, \left(B \cap\ C\right)=80 \)
\( \Large n \left(H \cap\ C\right)=40,\ n \left(C \cap\ H \cap\ B\right)=24 \)
Therefore, \( \Large n \left(C^{c} \cap\ H^{c} \cap\ B^{c}\right)=n\left[ \left(C \cup\ H \cup\ B\right)^{c} \right] \)
= \( \Large n \left(u\right)-n \left(C \cup\ H \cup\ B\right) \)
= \( \Large 800 - \left[ n \left(C\right)+n \left(H\right)+n \left(B\right)-n \left(H \cap
\ C\right)-n \left(H \cap\ B\right)-n \left(C \cap\ B\right)+n \left(C \cap\ H \cap\ B\right) \right] \)
= \( \Large 800-\left[ 224+240+336-40-64-80+24 \right] \)
= \( \Large 800 - 640 = 160 \)
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