In a class of 40 students, 8 students only like basketball only, 7 students only like volleyball only. 10 students only like soccer, but there are 12 students not only like soccer, but also like basketball or volleyball or both. There is 1 student doesn't like any sports, and 11 students like exactly two sports. Among those 11 students, 4 of them don't like basketball. Find the number of students who like basketball and soccer only.
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2006-10-25 4:33 am
回答 (2)
2006-10-25 7:36 am
✔ 最佳答案
note that total number of students liking at least 1 sport = 40 - 1 = 39basketball = 8
volleyball = 7
soccer = 10
now there are 14 students left who like 2 sports or more
since there are 12 students not only like soccer, but like basketball or volleyball or both
therefore, 2 students like basketball + volleyball
i.e. basketball + volleyball = 2
now there are 12 students who like soccer and like 2 or 3 sports
since 11 students like exactly two sports, where 2 of them are basketball + volleyball
therefore, 3 students like all 3 sports(12 - (11 - 2) = 3)
i.e. basketball + volleyball + soccer = 3
now there are 9 students who like soccer and one other sport
since 4 of them do not like basketball
therefore, 4 students like soccer + volleyball and 5 students like soccer + basketball
i.e. soccer + volleyball = 4
soccer + basketball = 5
2006-10-25 7:53 am
The no. of students who like at least two kinds of sports
= total no. of students of the class - students who like one sport only - students who does not like sport
= 40 - 8 - 7 - 10 - 1
= 14
The no. of students who like at least two kinds of sports
= students like exactly two sports + students like exactly three sports
So, students like exactly three sports
= 14 -11 = 3
Among those 11 students who like exactly two sports, 4 of them do not like basketball.
So, these 4 students like soccer and volley ball only. ------------(A)
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students not only like soccer, but also like basketball or volleyball or both
+ students not like soccer, but like both basketball and volleyball
= The no. of students who like at least two kinds of sports
2 + students not like soccer, but like both basketball and volleyball
= 14
So, students not like soccer, but like both basketball and volleyball
= 14 - 12 = 2
So, students like basketball and volleyball only
= 2 ------------------------(B)
From (A), (B),
So, students like basketball and soccer only
= 11 students like exactly two sports - like soccer and volley ball only - like basketball and volley ball only
= 11 - 4 - 2
= 5
= total no. of students of the class - students who like one sport only - students who does not like sport
= 40 - 8 - 7 - 10 - 1
= 14
The no. of students who like at least two kinds of sports
= students like exactly two sports + students like exactly three sports
So, students like exactly three sports
= 14 -11 = 3
Among those 11 students who like exactly two sports, 4 of them do not like basketball.
So, these 4 students like soccer and volley ball only. ------------(A)
----------------------------------
students not only like soccer, but also like basketball or volleyball or both
+ students not like soccer, but like both basketball and volleyball
= The no. of students who like at least two kinds of sports
2 + students not like soccer, but like both basketball and volleyball
= 14
So, students not like soccer, but like both basketball and volleyball
= 14 - 12 = 2
So, students like basketball and volleyball only
= 2 ------------------------(B)
From (A), (B),
So, students like basketball and soccer only
= 11 students like exactly two sports - like soccer and volley ball only - like basketball and volley ball only
= 11 - 4 - 2
= 5
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