Choosing Class Representatives: A Combination Problem

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Homework Help Overview

The problem involves selecting a team of 5 class representatives from a group of 33 students, specifically 20 girls and 13 boys, with the requirement of choosing 3 girls and 2 boys. Participants are discussing the calculation of combinations to determine the number of ways to form this team.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of combinations, specifically the formula nCr, and the correct application of values for n and r. There are questions about whether the original poster is counting all possible 5-person committees or just the specified combination of representatives.

Discussion Status

Some participants confirm the calculations provided by the original poster, while others emphasize the importance of understanding the reasoning behind the questions asked. There is a focus on ensuring that the original poster comprehends the process rather than just arriving at a numerical answer.

Contextual Notes

There is mention of the original poster's unfamiliarity with the combination concept, which may influence their understanding of the problem. Additionally, the discussion touches on the importance of showing intermediate steps in calculations for clarity and potential partial credit in academic settings.

mtayab1994
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Homework Statement



A class consists of 33 students 20 girls and 13 boys.


Homework Equations



We want to choose a team of 5 class representatives consisting of 3 girls and 2 boys.

What is the possibility of choosing the 5 people.

The Attempt at a Solution



Using the combination definition i got: nCr=nPr/r! I got total of 88920 combinations . Is that correct.
 
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hi mtayab1994! :smile:
mtayab1994 said:
A class consists of 33 students 20 girls and 13 boys.
…
Using the combination definition i got: nCr=nPr/r! I got total of 88920 combinations . Is that correct.

(that's 20C3*13C2)

yes :smile:

(is anything worrying you about that?)
 
tiny-tim said:
hi mtayab1994! :smile:


(that's 20C3*13C2)

yes :smile:

(is anything worrying you about that?)

Not really, I just haven't learned it yet in school that's why I'm just trying to make sure.
 
mtayab1994 said:

Homework Statement



A class consists of 33 students 20 girls and 13 boys.


Homework Equations



We want to choose a team of 5 class representatives consisting of 3 girls and 2 boys.

What is the possibility of choosing the 5 people.

The Attempt at a Solution



Using the combination definition i got: nCr=nPr/r! I got total of 88920 combinations . Is that correct.

What are the n and r are you using in this formula? Is n = 33? Is r = 5? If so, you are counting all the 5-person committees. Is that what the question asked?

RGV
 
Ray, see my post …
tiny-tim said:
(that's 20C3*13C2)

… I did that to save you having to check! :wink:
 
tiny-tim said:
Ray, see my post …


… I did that to save you having to check! :wink:

Actually, it is important for the OP to answer the questions and to think about why people ask them! You and I both know the answer; does the OP know it?

RGV
 
Ray Vickson said:
does the OP know it?

yes, because he got the right answer :smile: (which i was confirming) …

the other answer would have been 237336 :wink:​
 
tiny-tim said:
yes, because he got the right answer :smile: (which i was confirming) …

the other answer would have been 237336 :wink:​

OK, but another point (that I hope the OP gets) is the merit of showing some intermediate steps. Some instructors/TAs require that, and perhaps some do not, but it is always a good idea. A common situation is when a student writes down the intermediate step correctly but then makes an arithmetic error (or copies the results incorrectly) and so gets an incorrect final numerical answer. If he/she just writes down the number, and it is wrong, the question gets 0, but if an intermediate step is written the question may (depending on policy, etc.) get part marks---the theory being that the student seems to know what he/she is doing but just made a simple arithmetic mistake. Of course, the student needs to fit the requirements to the syllabus, but being explicit and communicating effectively cannot do any harm.

Also: as to your point about the 'right answer': I have seen it happen a few times over the years that a student uses the wrong formula, makes an arithmetic error and for that reason gets the right answer!

RGV
 

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