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There are 5 students in an English class. The English instructor wants to hold a debate in the class in all possible groups of 2 students such that 1 student presents the case “FOR” and the other student presents the case “AGAINST”. Each student can debate with the other student only once. How many topics will the teacher need such that possible each pair gets a different topic?
- a)5
- b)10
- c)15
- d)20
- e)40
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
There are 5 students in an English class. The English instructor wants...
Step 1: Understand the objective
The objective of the question is to find the number of different debate topics the teacher will need.
And the information provided to us is:
- There are 5 students in the class.
- Each student debates with every other student only once.
Step 2: Write the objective equation enlisting all tasks
We need to complete the following task to accomplish the objective:
Task 1 – Make groups of 2 students by selecting 2 students from 5 students.
Thus, the Objective Equation will be:
(Number of different debate topics needed) = (Number of ways of selecting 2 students from 5 students)
Step 3: Determine the number of ways of doing each task
The number of ways in which the task can be performed = 5C2 = 10
Step 4: Calculate the final answer
Thus the teacher can make 10 groups of 2 students and hence will need to get 10 different topics.
Correct Answer: Option B
Most Upvoted Answer
There are 5 students in an English class. The English instructor wants...
Understanding the Problem
To determine how many topics the teacher needs, we first need to find out how many different pairs of students can be formed from the group of 5 students. Each pair will require a unique debate topic.
Calculating the Number of Pairs
- We can use the combination formula to find the number of ways to choose 2 students from a group of 5. The formula for combinations is given by:
C(n, k) = n! / (k!(n-k)!)
- Here, n = 5 (total students) and k = 2 (students in each debate).
- Plugging in the values:
C(5, 2) = 5! / (2!(5-2)!) = 5! / (2! * 3!)
- This simplifies to:
C(5, 2) = (5 × 4) / (2 × 1) = 20 / 2 = 10
Conclusion
- The result shows that there are 10 unique pairs of students.
- Since each pair requires a different topic for their debate, the teacher will need 10 different topics.
Final Answer
- Therefore, the correct answer is option 'B': 10.
To determine how many topics the teacher needs, we first need to find out how many different pairs of students can be formed from the group of 5 students. Each pair will require a unique debate topic.
Calculating the Number of Pairs
- We can use the combination formula to find the number of ways to choose 2 students from a group of 5. The formula for combinations is given by:
C(n, k) = n! / (k!(n-k)!)
- Here, n = 5 (total students) and k = 2 (students in each debate).
- Plugging in the values:
C(5, 2) = 5! / (2!(5-2)!) = 5! / (2! * 3!)
- This simplifies to:
C(5, 2) = (5 × 4) / (2 × 1) = 20 / 2 = 10
Conclusion
- The result shows that there are 10 unique pairs of students.
- Since each pair requires a different topic for their debate, the teacher will need 10 different topics.
Final Answer
- Therefore, the correct answer is option 'B': 10.
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There are 5 students in an English class. The English instructor wants to hold a debate in the class in all possible groups of 2 students such that 1 student presents the case “FOR” and the other studentpresents the case “AGAINST”. Each student can debate with the other student only once. How many topics will the teacher need such that possible each pair gets a different topic?a)5b)10c)15d)20e)40Correct answer is option 'B'. Can you explain this answer?
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