A) 43
B) 76
C) 49
D) None of these
Correct Answer: A
Solution :
Let C, H, F denote the sets of members who are on the cricket team, hockey team and football team respectively. Then we are given \[\operatorname{n}(C)=21, n(H) = 26, n(F)= 29\] \[\operatorname{n}(H\cap C)=14,\,n\left( H\cap F \right)=15,n\left( F\cap C \right)=12\] and \[\operatorname{n}\left( C\cap H\cap F \right)=8.\] We have to find \[\operatorname{n}\left( C\cup H\cup F \right)\] To find this, we use the formula \[\operatorname{n}\left( C\cup H\cup F \right)=\,\,n(C) + n(H) + n(F)\] \[-\operatorname{n}\left( C\cap H \right)-n\left( H\cap F \right)-n\left( F\cap C \right)+n\left( C\cap H\cap F \right)\] Hence, \[\operatorname{n}\left( C\cup H\cup F \right)\] \[=\left( 21\text{ }+26+29 \right)-\left( 14+\text{ }15+12 \right)4-8=43\] Thus these are 43 members in all.You need to login to perform this action.
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