# Homework Help: Counting Problem

1. Oct 4, 2011

### Punkyc7

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: Oct 4, 2011
2. Oct 4, 2011

### flyingpig

clarify the problem

"how many ways and you..."

what does that mean?

3. Oct 4, 2011

### Punkyc7

meant to same can you

4. Oct 4, 2011

### flyingpig

I think it's a combinatorics problem, it doesn't say how the poles are arranged.

5. Oct 4, 2011

### Punkyc7

The poles dont move the flags on the poles move

6. Oct 4, 2011

### flyingpig

Oh sorry I was thinkig about a stand.

In that case I think 8C3 isn't wrong.

7. Oct 4, 2011

### Punkyc7

At least part of it is right...I just dont know how to verify it. I was thinking something with T numbers but I couldnt see how to work them in. So I just thought of what you could do.

8. Oct 4, 2011

### flyingpig

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 gotta add more combinations.

9. Oct 4, 2011

### Punkyc7

huh? what do you mean?

Last edited: Oct 4, 2011