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Q.

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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a

42

b

43

c

45

d

none of these

answer is B.

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Detailed Solution

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.
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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