Solving 8 Flag Placement Problem on 3 Poles

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Homework Help Overview

The problem involves determining the number of ways to place 8 distinct flags on 3 distinct poles, with the condition that no pole can be empty. Participants are exploring combinatorial approaches to solve this problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use combinations and permutations to calculate the arrangements, suggesting a formula involving 8C3 and permutations of flags. Some participants question the clarity of the problem statement and the assumptions about the arrangement of poles and flags.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the problem and questioning each other's reasoning. Some guidance has been offered regarding the combinatorial aspects, but there is no explicit consensus on the correct approach or solution yet.

Contextual Notes

Participants are grappling with the interpretation of the problem, particularly regarding the arrangement of poles and the implications of having no empty poles. There is also uncertainty about how to verify the proposed methods and calculations.

Punkyc7
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How many ways can you place 8 distinct flags on 3 distinct poles if no pole can be empty.Im not sure how to approach this problem because writing out all the possibilities would take a lot of time
So I was thinking it would be something like

8C3 to select the three flags that have to be placed.

Then you could take any permutation of the flags on the poles to get 3!

From there I was thinking that you could take the remaining flags and just place them on any of the poles

This is what I got

8C3 * 3!* 3^(5)

I am not sure if it is right though
 
Last edited:
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clarify the problem

"how many ways and you..."

what does that mean?
 
meant to same can you
 
I think it's a combinatorics problem, it doesn't say how the poles are arranged.
 
The poles don't move the flags on the poles move
 
Punkyc7 said:
The poles don't move the flags on the poles move

Oh sorry I was thinkig about a stand.

In that case I think 8C3 isn't wrong.
 
At least part of it is right...I just don't know how to verify it. I was thinking something with T numbers but I couldn't see how to work them in. So I just thought of what you could do.
 
Punkyc7 said:
At least part of it is right...I just don't know how to verify it. I was thinking something with T numbers but I couldn't see how to work them in. So I just thought of what you could do.

Here is how I think about it. If it removes the condition that it can have 2 flagged flags and one empty pole, then you got to add more combinations.
 
huh? what do you mean?
 
Last edited:

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