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In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60 students participate in both activities. How many students are involved in either band or sports?
- a)300 students
- b)225 students
- c)150 students
- d)Can’t be determined
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In a school of 320 students, 85 students are in the band, 200 students...
Given information:
Total number of students in the school = 320
Number of students in the band = 85
Number of students on sports teams = 200
Number of students who participate in both activities = 60
To find:
Number of students involved in either band or sports
Solution:
We can use the inclusion-exclusion principle to find the number of students involved in either band or sports.
Total number of students involved in either band or sports = Number of students in band + Number of students on sports teams - Number of students who participate in both activities
Substituting the given values, we get:
Total number of students involved in either band or sports = 85 + 200 - 60
= 225
Therefore, the correct answer is option B - 225 students.
Explanation:
The inclusion-exclusion principle is a counting technique used to find the size of a set that is a union of two or more sets. The formula for the principle is:
|A ∪ B| = |A| + |B| - |A ∩ B|
where |A| represents the number of elements in set A, and |A ∩ B| represents the number of elements common to both sets A and B.
In this problem, the sets A and B represent the students in the band and on sports teams, respectively. The union of these sets represents the students involved in either band or sports.
We are given the values of |A|, |B|, and |A ∩ B|, and we can use the formula to find |A ∪ B|. This gives us the total number of students involved in either band or sports.
Total number of students in the school = 320
Number of students in the band = 85
Number of students on sports teams = 200
Number of students who participate in both activities = 60
To find:
Number of students involved in either band or sports
Solution:
We can use the inclusion-exclusion principle to find the number of students involved in either band or sports.
Total number of students involved in either band or sports = Number of students in band + Number of students on sports teams - Number of students who participate in both activities
Substituting the given values, we get:
Total number of students involved in either band or sports = 85 + 200 - 60
= 225
Therefore, the correct answer is option B - 225 students.
Explanation:
The inclusion-exclusion principle is a counting technique used to find the size of a set that is a union of two or more sets. The formula for the principle is:
|A ∪ B| = |A| + |B| - |A ∩ B|
where |A| represents the number of elements in set A, and |A ∩ B| represents the number of elements common to both sets A and B.
In this problem, the sets A and B represent the students in the band and on sports teams, respectively. The union of these sets represents the students involved in either band or sports.
We are given the values of |A|, |B|, and |A ∩ B|, and we can use the formula to find |A ∪ B|. This gives us the total number of students involved in either band or sports.
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Community Answer
In a school of 320 students, 85 students are in the band, 200 students...
N(A)= 200,n(B)=85,n(A ∩ B)=60
as n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
=200+85-60=225
as n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
=200+85-60=225
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In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60 students participate in both activities. How many students are involved in either band or sports?a)300 studentsb)225 studentsc)150 studentsd)Can’t be determinedCorrect answer is option 'B'. Can you explain this answer?
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