Answer to Question #285500 in Discrete Mathematics for feey

Question

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

Answer 1

Given n(c)=21 and n(H⋂C)=14

n(H)=26 and n(H⋂F)=15

n(F)=29 and n(H⋂F⋂C)=8

∴n(C⋃H⋃F)=n(C)+n(H)+n(F)−n(H⋂C)−n(H⋂F)

−n(F⋂C)+n(H⋂F⋂C)

=21+26+29−14−15−12+8

=84−41

=43