I'm lost with this verbal math problem

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NotGreatAtMath

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Nov 21, 2019
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So there is this hard problem I tried to solve, but I had no idea what to do.


The problem:

There are
8 Greek
10 American
15 Russian
16 Chinese
22 Canadian students.

Students study in groups.
A group is made up from one or more students.
If there are two or more students of the same nationality in a group, there must be at least one student of another nationality in the group.

In how many ways can 71 students divide the group?


I guess I should do some combination stuff
1574341845951.png Maybe use this fancy formula. idk.

I'm totally lost, any help would be appreciated :)
 
I assume this is for a class. What have you learned so far about combinatorics besides the combination formula? This sounds like it would be far beyond that. (When a student says "this is a hard problem", I usually expect it to be easy, for me, but this one is not immediately obvious ...)

The wording also doesn't sound quite as precise as I would expect; did you tell us the exact wording of the problem? It looks like you are using "the group" in two different ways (the whole collection, and any one study group). I assume students are considered distinguishable, but that is not clearly stated.

One possible strategy would be subtraction: count all possible divisions into groups (that is, partitions into any number of subsets), and subtract those that don't meet the requirements.
 
It isn't for a class so it's beyond my math knowledge. I translated the problem into english, so the wording isn't perfect. I meant In how many ways can 71 students divide the group? In how many different ways can the students be divided into groups? Like how many different possible arrangments there are. I think the students are supposed to be distinguishable.
 
Last edited:
NotGreatAtMath said:
The problem:
There are
8 Greek
10 American
15 Russian
16 Chinese
22 Canadian students.
Students study in groups.
A group is made up from one or more students.
If there are two or more students of the same nationality in a group, there must be at least one student of another nationality in the group.
In how many ways can 71 students divide the group?
Click to expand...
You have used "the group" and "groups" in interchangeable ways.
We need clarification as the number of study groups. Are all students assigned to a group?
Are there are a fixed number of study groups?
Please do clarify your post.
 
I tried to rewrite the problem:

There are
8 Greek
10 American
15 Russian
16 Chinese
22 Canadian students.

Students study in groups. All students must be assigned into groups.
A group is made up from one or more students.
If there are two or more students of the same nationality in a group, there must be at least one student of another nationality in that group.
There is not a fixed number of groups.

In how many different ways can 71 students be divided into groups? How many different possible arrangements are there?
 
NotGreatAtMath said:
It isn't for a class so it's beyond my math knowledge. I translated the problem into english, so the wording isn't perfect. I meant In how many ways can 71 students divide the group? In how many different ways can the students be divided into groups? Like how many different possible arrangments there are. I think the students are supposed to be distinguishable.
Click to expand...
It isn't for a class so it's beyond my math knowledge.

Why are you trying to solve this problem?

We need to know the depth of your math knowledge - so that our answers will make sense to you.

If you are posting for somebody else, please let us interact with the "student".
 
It is not hard to create a problem that is impossible to solve apart from just writing a computer program to list all the possibilities. I'm not saying this is that bad, but it may be, if you invented it.

On the other hand, you say you translated the problem from somewhere, rather than just making it up; knowing where it came from would help us determine whether it makes any sense to even try to solve it, or to explain a solution to someone without any background.

As has been asked, why do you want to solve this? Tell us more about it.
 
NotGreatAtMath said:
I tried to rewrite the problem:
There are
8 Greek
10 American
15 Russian
16 Chinese
22 Canadian students.
Students study in groups. All students must be assigned into groups.
A group is made up from one or more students.
If there are two or more students of the same nationality in a group, there must be at least one student of another nationality in that group.
There is not a fixed number of groups. In how many different ways can 71 students be divided into groups? How many different possible arrangements are there?
Click to expand...
The way it is now written there can be anywhere from one to seventy-one different study groups.
That is a computational nightmare. With writing a fairly involve computer program, I doubt it is possible to solve.
 
Well there was this interactive live tv game show thing where one way to compete was to solve a similar math problem to this. Then you could subtract some 80-digit number from the answer, convert that answer's numbers to letter with ASCII and arrange the letters to get the answer or something like that.
 
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