In a school of 800 boys,224 play cricket,240 | 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(U) = 800$$n(C) = 224, n(H) = 240, n(B)

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(U) = 800$$n(C) = 224, n(H) = 240, n(B) = 336$$n(B \cap H) = 64, n(C \cap B) = 80, n(C \cap H) = 40$$n(C \cap H \cap B) = 24$Using the Principle of Inclusion-Exclusion:$n(C \cup H \cup B) = n(C) + n(H) + n(B) - [n(C \cap H) + n(H \cap B) + n(C \cap B)] + n(C \cap H \cap B)$$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 do not play any game is $n(U) - n(C \cup H \cup B) = 800 - 640 = 160$.

In a school of $800$ boys,$224$ play cricket,$240$ play hockey,and $336$ play basketball. Of the total,$64$ play basketball and hockey,$80$ play cricket and basketball,and $40$ play cricket and hockey,while $24$ play all three games. Find the number of boys who do not play any game.

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