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In a group of athletic teams in a school, 21 are in the basketball team, 26 in the hockey team and 29 in the football team. If 14 play hockey and basketball, 12 play football and basketball, 15 play hockey and football, 8 play all the three games, then how many play football only ?
- a)10
- b)29
- c)21
- d)18
- e)None of the above/More than one of the above
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
In a group of athletic teams in a school, 21 are in the basketball tea...
Given Data:
Total number of students in the athletic teams:
- Basketball team: 21
- Hockey team: 26
- Football team: 29
Overlap Data:
- 14 students play hockey and basketball
- 12 students play football and basketball
- 15 students play hockey and football
- 8 students play all three games
Calculation:
To find the number of students who play football only, we need to subtract the total number of students who play football (including overlap with other teams) from the total number of students in the football team.
- Total students who play basketball: 21 (given)
- Total students who play hockey: 26 (given)
- Total students who play football: 29 (given)
- Total students who play basketball and hockey: 14 (given)
- Total students who play basketball and football: 12 (given)
- Total students who play hockey and football: 15 (given)
- Total students who play all three games: 8 (given)
- Total students who play basketball, hockey, and football: 8 (given)
Now, we can calculate the total number of students who play football:
Total students who play football = Total football players - (Players in basketball and football + Players in hockey and football - Players in all three teams)
Total students who play football = 29 - (12 + 15 - 8)
Total students who play football = 29 - 19
Total students who play football = 10
Therefore, 10 students play football only. Hence, the correct answer is option A) 10.
Total number of students in the athletic teams:
- Basketball team: 21
- Hockey team: 26
- Football team: 29
Overlap Data:
- 14 students play hockey and basketball
- 12 students play football and basketball
- 15 students play hockey and football
- 8 students play all three games
Calculation:
To find the number of students who play football only, we need to subtract the total number of students who play football (including overlap with other teams) from the total number of students in the football team.
- Total students who play basketball: 21 (given)
- Total students who play hockey: 26 (given)
- Total students who play football: 29 (given)
- Total students who play basketball and hockey: 14 (given)
- Total students who play basketball and football: 12 (given)
- Total students who play hockey and football: 15 (given)
- Total students who play all three games: 8 (given)
- Total students who play basketball, hockey, and football: 8 (given)
Now, we can calculate the total number of students who play football:
Total students who play football = Total football players - (Players in basketball and football + Players in hockey and football - Players in all three teams)
Total students who play football = 29 - (12 + 15 - 8)
Total students who play football = 29 - 19
Total students who play football = 10
Therefore, 10 students play football only. Hence, the correct answer is option A) 10.
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Community Answer
In a group of athletic teams in a school, 21 are in the basketball tea...
The number of players in the different games are as follows:
From the question,
a + b + d + e = 21 ----(i)
c + b + e + f = 26 ----(ii)
d + e + f + g = 29 ----(iii)
b + e = 14 ----(iv)
d + e = 12 ----(v)
f + e = 15 ----(vi)
e = 8 ----(vii)
To obtain the number of players playing football only, we need to find the value of g.
From the Venn diagram,
d + e + f + g - (d + e) - (f + e - e) = 29 - 12 - (15 - 8) = 10
∴ The number of players playing football only are 10
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In a group of athletic teams in a school, 21 are in the basketball team, 26 in the hockey team and 29 in the football team. If 14 play hockey and basketball, 12 play football and basketball, 15 play hockey and football, 8 play all the three games, then how many play football only ?a)10b)29c)21d)18e)None of the above/More than one of the aboveCorrect answer is option 'A'. Can you explain this answer?
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