Question

(10) In a group of athletic teams in a school , 21
are in the basket ball team; 26 in the hockey
team and 29 in football team. If 14 play hockey
and basket ball; 12 play football and basket
ball; 15 play hockey and football and 8 play
all the three games. Find :
(i) how many players are there in all?Ans 13
(ii) how many play football only?Ans 10​

Answer 1

n(B)=21

n(H)=26

N(F)=29

n(H∩B)=14

n(F∩B)=12

n(H∩F)=15

n(B∩H∩F)=8

(i)n(B∪H∪F)=n(B)+n(H)+n(F)-n(B∩H)-n(H∩F)-n(B∩F)+n(B∩F∩H)

n(B∪H∪F)=21+26+29-14-12-15+8

n(B∪H∪F)= 43

(ii) n(F)=n((F∩B)-H)+n((F∩H)-B)+n(F∩B∩H)+n(F-(B∪H))

    n((F∩B)-H)= 4

    n((F∩H)-B)=7

These values can be found using venn diagram.

∴29=4+7+x

29-11=x

x=18

Therefore, 18 people play only football.

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