Find Total Members in Three Athletic Teams
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?
Solution
\[ n(B\cup H\cup F) \] \[ =n(B)+n(H)+n(F)-n(B\cap H)-n(H\cap F)-n(F\cap B)+n(B\cap H\cap F) \] \[ =21+26+29-14-15-12+8 \] \[ =43 \]Hence, the total number of members is
\[ \boxed{43} \]