Question

Out 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,$14$ three games.The total number of members in the three athletic

• A. $43$
• B. $49$
• C. $76$
• D. none of these

Answer 1

The correct option is A $43$

The question must be

Of the members of three athletic teams in a certain school, $21$ are in the basketball team, $26$ in the hockey team and $29$ in the football team. $14$ play hockey and basket ball, $15$ play hockey and football, $12$ play football and basketball and 8 play all the three games. How many members are there in all?

Solution:A total number of People $n\left(P\right)=$.

People who play Basketball $n\left(B\right)=21$.

People who play Football $n\left(F\right)=29$.

People who play Hockey $n\left(H\right)=26$.

People who play Basketball and Hockey $n(B\cap H)=14$

People who play Football and Hockey $n(H\cap F)=15$

People who play Basketball and Football $n(B\cap F)=12$

People who play all games. $n(H\cap B\cap F)=8$

Total number of people would be $n\left(HorBorF\right)=n(H\cup B\cup F)$

We know,

$n(H\cup B\cup F)=n\left(H\right)+n\left(B\right)+n\left(F\right)–n(H\cap B)–n(H\cap F)–n(B\cap F)+n(H\cap B\cap F)$

$n(H\cup B\cup F)=26+21+29–14–15–12+8$

$n(H\cup B\cup F)=43$.

Hence, there are $43$ members in all.