Question

Of the number of three athletic teams in a school, $21$ are in the basketball team, $26$ in hockey team and $29$ in the football team. $14$ play hockey and basketball, $15$ play hockey and football, $12$ play football and basketball and $8$ play all the games. The total number of members is

• A. $42$
• B. $43$
• C. $45$
• D. None of these

Answer 1

The correct option is B $43$

Let $B,H,F$ be the sets of members in the basket ball team, hockey team, football team respectively.
$\therefore n\left(B\right)=21,N\left(H\right)=26,n\left(F\right)=29,n(H\cap B)=14$,
$\therefore n(H\cap F)=15,n(F\cap B)=12,n(B\cap H\cap F)=8$.
$\therefore n(B\cup H\cup F)=n\left(B\right)+n\left(H\right)+n\left(F\right)-n(B\cap H)-n(H\cap F)-(B\cap F)+n(B\cap H\cap F)$
$=21+26+29-14-15-12+8=43$