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 basket ball, 15 play hockey and football, 12 play football and basketball and 8 play all the three games bow many members are there in all?

Answer 1

Let `B` is the set of members who are in basketball team, `F` is the set of members who are in Football team,
`H` is the set of members who are in hockey team.
Then,
`n(BuuFuuH) = n(B)+n(F)+n(H)-n(BnnF)-n(FnnH)-n(BnnH)+n(BnnFnnH)`
`:. n(BuuFuuH) = 21+26+29-14-15-12+8` `=>n(BuuFuuH) = 43`
So, there are total `43` members in all.