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Solve the following question and mark the best possible option.
 
Q. An institute has 5 departments and each department has 50 students. If students are picked up randomly from all 5 departments to form a committee, what should be the minim him number of students in the committee so that at least one department should have representation of minimum 5 students?
  • a)
    11
  • b)
    15
  • c)
    21
  • d)
    41
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?
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Solve the following question and mark the best possible option.Q. An i...
For representation of minimum 5 students from atleast one department, assume that first 5 students are selected, one from each department. Similarly, next 3 sets of 5 students will be selected (3 from each department). Now, 4 students are selected from each department. As soon as one more student is selected from any department, the representation of that department will be of 5 students. Hence, minimum 21 students should be in the committee.
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Solve the following question and mark the best possible option.Q. An i...
Understanding the Problem
In this problem, we have an institute with 5 departments, each containing 50 students. We need to form a committee by randomly selecting students from these departments. The goal is to ensure that at least one department has a minimum of 5 students represented in the committee.
Applying the Pigeonhole Principle
To solve this, we can utilize the Pigeonhole Principle. This principle states that if n items are put into m containers, with n > m, at least one container must hold more than one item. Here, the "items" are the students picked for the committee, and the "containers" are the departments.
Calculation Steps
1. Department Representation: We have 5 departments (containers).
2. Maximum without 5 in One Department: To avoid having 5 students in any one department, we can choose a maximum of 4 students from each department.
3. Total Students Selected: If we select 4 students from each of the 5 departments:
- 4 students/department * 5 departments = 20 students.
This means if we select 20 students, it is possible to have 4 students from each department, and no department would have 5 students.
Forming the Committee
4. Adding One More Student: To ensure that at least one department has 5 students, we need to add one more student to our selection.
- Therefore, 20 students + 1 additional student = 21 students.
Conclusion
Thus, the minimum number of students required in the committee to guarantee that at least one department has a representation of at least 5 students is 21. Hence, the correct answer is option C.
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Solve the following question and mark the best possible option.Q. An institute has 5 departments and each department has 50 students. If students are picked up randomly from all 5 departments to form a committee, what should be the minim him number of students in the committee so that at least one department should have representation of minimum 5 students?a)11b)15c)21d)41e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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