A) 43
B) 76
C) 49
D) None of these
Correct Answer: A
Solution :
[a] 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 \[n\,(C)=21,\]\[n\,(H)=26,\]\[n\,(F)=29\] \[n\,(H\cap C)=14,\]\[n\,(H\cap F)=15,\] \[n\,(F\cap B)=12\] and\[n\,(C\cap H\cap F)=8\] We have to find \[n\,(C\cup H\cup F).\] To find this, we use the formula \[n\,(C\cup H\cup F)=n\,(C)+n\,(H)+n\,(F)\] \[-\,n\,(C\cap H)-n\,(H\cap F)\] \[-n\,(F\cap C)+n\,(C\cap H\cap F)\] Hence, \[n\,(C\cup H\cup F)=(21+26+29)\] \[-\,(14+15+12)+8=43\] Thus, there are 43 members in all. |
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