Choosing Class Representatives: A Combination Problem

[mtayab1994]

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.

 

[tiny-tim]

hi mtayab1994!

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

(is anything worrying you about that?)

 

[mtayab1994]

hi mtayab1994!


(that's ²⁰C₃*¹³C₂)

yes

(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.

 

[Ray Vickson]

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

 

[tiny-tim]

Ray, see my post …

(that's ²⁰C₃*¹³C₂)

… I did that to save you having to check!

 

[Ray Vickson]

Ray, see my post …


… I did that to save you having to check!

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

 

[tiny-tim]

does the OP know it?

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

the other answer would have been 237336 ​

 

[Ray Vickson]

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

the other answer would have been 237336 ​

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