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 play hockey and cricket, 15 play hockey and football, 12 play football and cricket and 8 play all the three games. The total number of members in the three athletic teams is:

Formula used:

n(B U H U F) = n(B) + n(H).n(F) − n(B ∩ H) − n(H ∩ F) − n(F ∩ B) + n(B ∩ H ∩ F).

Calculation:

Let B, H, F denote the sets of members who are in the basket hall team, hockey team and football team respectively. 

Given n(B) =21, n(H)= 2 6, n(F) = 29. 

n(H∩B) = 14, n (H∩F) = 15, n(F∩B) = 12 and n(B ∩ H ∩ F) = 8.

We have to find n(B U H U F) i.e. The total number of members in the three athletic teams.

n(B U H U F) = n(B) + n(H).n(F) − n(B ∩ H) − n(H ∩ F) − n(F ∩ B) + n(B ∩ H ∩ F).

n(B U H U F) = (21 + 26 + 29) − (14 + 15 + 12) + 8 = 43