Of the number of three athletic teams in a 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 games. The total number of members is

Question

Of the number of three athletic teams in a 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 games. The total number of members is

Infinity Learn · Accepted Answer

Let B,H,F be the sets of the three teams respectivelyso $$n(B)=21$$,$$n(H)=26$$,$$n(F)=29$$,$$n(H$$∩$$B)=14n(H$$∩$$F)=15$$,$$n(F$$∩$$B)=12n(B$$∩H∩$$F)=8and$$  $$n(B$$∪H∪$$F)=n(B)+n(H)+n(F)$$−$$n(H$$∩$$B)$$−$$n(H$$∩$$F)$$−$$n(F$$∩$$B)+n(B$$∩H∩$$F)=21+26+29$$−$$14$$−$$15$$−$$12+8=43$$.

Of the number of three athletic teams in a 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 games. The total number of members is

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Of the number of three athletic teams in a 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 games. The total number of members is

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Of the number of three athletic teams in a 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 games. The total number of members is