Question

Of the members of three athletic teams in a certain 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 three games how many members are there in all?

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

Answer 1

The correct option is A

$43$

Explanation for the correct option:

Finding the total number of members in all:

B is the set of members who are in the basketball, F is the set of members who are in the football and H is the set of members who are in the hockey.

Given,

Basketball team $n\left(B\right)=21$

Hockey team $n\left(H\right)=26$

Football team $n\left(F\right)=14$

Hockey and basketball $n\left(H\cap B\right)=14$ members

Hockey and football $n\left(H\cap F\right)=15$ members

Football and basketball $n\left(F\cap B\right)=12$ members

All three games $n\left(F\cap B\cap H\right)=8$ members

Number of members there in all is given by,

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

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

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

So, there are $43$ members in all.

Hence, option(A) is the correct answer.