Single Choice

Of the members of three athletic teams in a school $$21$$ are in the cricket team, $$26$$ are in the hockey team and $$29$$ are in the football team. Among them, $$14$$ play hockey and cricket, $$15$$ play hockey and foot ball, and $$12$$ play foot ball and cricket. Eight play all the three games. The total number of members in the three athletic teams is

A$$43$$
Correct Answer
B$$76$$
C$$49$$
D$$61$$

Solution

Given, $${ n }({ C })=21,{ n }({ H })=26,,{ n }({ F })=29$$
Also, $${ n }({ H }\cap { C })=14, { n }({ H }\cap { F })=15, { n }({ F }\cap { C })=12,{ n }({ F }\cap { C }\cap { H })=8$$
Now, $$n(C\cup F\cup H)=n(C)+n(F)+n(H)-n(C\cap F)-n(F\cap H)-n(C\cap H)+n(C\cap F\cap H)$$
$$\Rightarrow n(C\cup F\cup H)=43$$
Total number of players $$=43$$

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