Combinations of Selecting Students

In summary, there are 22,800 ways to select 2 females and 3 males from a class of 30 students with 20 females and 10 males. This can be calculated by using the multiplication principle and the combinations formula.
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Homework Statement


In how many ways can 2 females and 3 males be selected from a class of 30 with 20 female and 10 male students?

Homework Equations

The Attempt at a Solution


I saw this as a two step process. Step 1 being I have N1 ways of choosing 2 females and step 2 N2 ways of choosing 3 male. This means I can apply the multiplication principle using N1*N2.

I have 20C2 ways for the female and 10C3 for the males. Using the multiplication principles I get (20C2) * (10C3) = 22,800 ways.

I'm fairly confident in my answer, I just want to be sure I'm understanding the concepts behind it, thanks.
 
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You are correct.
 
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Related to Combinations of Selecting Students

1. How do combinations differ from permutations when selecting students?

Combinations involve selecting a group of items without regard to order, while permutations involve selecting items in a specific order. When selecting students, combinations would be used to choose a group of students for a project or team, while permutations would be used to determine the order of students for presentations or performances.

2. What is the formula for calculating the number of combinations when selecting from a group of students?

The formula for combinations is nCr = n! / (r!(n-r)!), where n represents the total number of students and r represents the number of students being selected.

3. Can the same student be selected for multiple combinations?

Yes, the same student can be selected for multiple combinations unless there are specific restrictions in place. In a random selection process, the chances of a student being selected for multiple combinations are the same as any other student in the group.

4. How can combinations be used in the classroom to promote diversity?

Combinations can be used to ensure that a diverse group of students is selected for projects or teams. By using a random selection process, combinations can help prevent bias and promote inclusivity in the classroom.

5. Are there any limitations to using combinations for selecting students?

One limitation is that combinations do not take into account individual strengths or weaknesses of students. It is possible that a group selected through combinations may not have a balanced distribution of skills or expertise. Additionally, it is important to consider any potential conflicts or compatibility issues between students when forming groups using combinations.

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