Out of 800 boys in a school,224 played cricke | vedclass

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(D) Let $C$,$H$,and $B$ represent the sets of boys who play cricket,hockey,and basketball,respectively.Given:$n(C) = 224, n(H) = 240, n(B) = 336$$n(H

Vedclass · Accepted Answer

$160$

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(D) Let $C$,$H$,and $B$ represent the sets of boys who play cricket,hockey,and basketball,respectively.Given:$n(C) = 224, n(H) = 240, n(B) = 336$$n(H \cap B) = 64, n(C \cap B) = 80, n(C \cap H) = 40$$n(C \cap H \cap B) = 24$Total boys $n(U) = 800$Using the Principle of Inclusion-Exclusion:$n(C \cup H \cup B) = n(C) + n(H) + n(B) - n(C \cap H) - n(H \cap B) - n(C \cap B) + n(C \cap H \cap B)$$n(C \cup H \cup B) = 224 + 240 + 336 - 40 - 64 - 80 + 24$$n(C \cup H \cup B) = 800 - 184 + 24 = 640$The number of boys who did not play any game is $n(U) - n(C \cup H \cup B) = 800 - 640 = 160$.

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 three games. The number of boys who did not play any game is:

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