Question

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. $43$
• B. $76$
• C. $49$
• D. $61$

Answer 1

The correct option is A $43$

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