Math Grouping Help: 20 Students, 4 Groups of 5, Different Schools

  • Thread starter ritwik06
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This would be 4! = 24 ways. In summary, there are 24 ways to divide 20 students into 4 groups of 5 and send them to 4 different schools.
  • #1
ritwik06
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Homework Statement



Divide 20 students in 4 groups of 5 each. Find the number of ways of doing this?
Also find how can these gropus be sent to 4 different schools?

The Attempt at a Solution



I get both the answers as:
20C5*15C5*10C5*5C5

But my book gives two different answers for the above 2 different question. Help Please!
 
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  • #2


The first answer looks correct: you first pick 5 out of 20 for the first group, then 5 out of the remaining 15 for the second group, etc.

For the second question, I think you should forget about the students. You have 4 groups, and 4 schools to send them to. In abstract terms: you have 4 balls and 4 slots, how many possible ways are there to put each ball into one slot?
 
  • #3


I would suggest approaching this problem using a systematic and logical approach. First, let's clarify the problem statement. It states that there are 20 students who need to be divided into 4 groups of 5 each. This means that each group will have 5 students. Now, the first question asks for the number of ways this can be done. In other words, how many different combinations of 5 students can be formed from a group of 20 students? This can be calculated using the combination formula, 20C5, which results in 15,504 possible ways.

For the second question, we need to consider the fact that the groups will be sent to 4 different schools. This means that each school will have a group of 5 students. So, we need to find the number of ways we can distribute these 4 groups of 5 students among the 4 schools. This can be calculated using the permutation formula, 4P4, which results in 24 possible ways.

Therefore, the two answers are different because they are solving for different scenarios. The first question is asking for the number of ways to divide 20 students into 4 groups of 5 each, while the second question is asking for the number of ways to distribute 4 groups of 5 students among 4 schools. It is important to carefully read and understand the problem statement in order to accurately solve the problem.
 

1. How do you group the 20 students into 4 groups of 5?

The 20 students can be divided into 4 groups of 5 in different ways. One way is to randomly assign the students to each group. Another way is to group students based on their similar skill levels or learning styles. The grouping method will depend on the purpose of the activity or lesson.

2. Is it better to have groups from the same school or mix students from different schools?

It ultimately depends on the goal of the activity or lesson. Having groups from the same school may foster a sense of familiarity and comfort among the students. On the other hand, mixing students from different schools can promote diversity and encourage collaboration among students from different backgrounds.

3. How do you ensure fairness in the grouping process?

In order to ensure fairness, it is important to establish clear criteria for grouping the students. This could include factors such as academic performance, social skills, or even a random selection process. It is also important to communicate the grouping method to the students and address any concerns they may have.

4. Can the grouping be changed if it is not working?

Absolutely. It is important to regularly assess and evaluate the effectiveness of the grouping method. If the groups are not working well together or the students are not benefiting from the grouping, it is important to be flexible and make necessary adjustments.

5. Are there any potential challenges with grouping students for math activities?

Some potential challenges with grouping students for math activities include balancing student abilities within groups, addressing potential conflicts or communication issues within the groups, and ensuring equal participation and engagement from all students. It is important to address these challenges and make adjustments as needed to promote a positive and effective learning experience for all students.

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