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.
