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?
A total number of People n(P) = ?.
People who play Basketball n(B) =21.
People who play Football n(F) = 29.
People who play Hockey n(H) = 26.
People who play Basketball and Hockey n(B ∩ H) = 14
People who play Football and Hockey n(H ∩ F) = 15
People who play Basketball and Football n(B ∩ F) = 12
People who play all games. n(H ∩B ∩ F) = 8
Total number of people would be n(H or B or F) = n(H∪B∪F)
We know,
n(H∪B∪F) = n(H)+n(B)+n(F) – n (H ∩ B)– n (H ∩ F)– n (B ∩ F)+ n (H ∩B ∩ F)
n(H∪B∪F) = 26+21+29–14–15–12+8
n(H∪B∪F) = 43.
Hence, there are 43 members in all.