TopScore QR Test 1, Question #5

[ILikeTeeth]

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Hello,

I hope someone can help.

The question is as follows:

How many arrangements can six people be seated round a circular table?

Thank you

 

[bpenly]

I believe the answer is 5! (you eliminate 1 person from the computation because it is a circular table).

So 5! = 5x4x3x2x1 = 120

 

[boogaking]

At the moment I am confused about that reasoning... probably something simple im looking over but ....why can't you fit 6 ppl around a circular table... so have having 6 spots around a round table???? thanks

 

[Rezdawg]

You can fit 6 people around a table...but look at it this way.

Lets say you have people, numbered 1, 2, 3, 4, 5, and 6. A random order could have them arranged like this...

3, 2, 5, 6, 1, 4

Because the table is circular, that would be the same as the following order...

6, 1, 4, 3, 2, 5

Can you see that? Im not sure if this is clear at all. You can look at it on a smaller scale. Take a table of 3 people, and look at the total number of combinations...

1) 1, 2, 3
2) 1, 3, 2
3) 2, 1, 3
4) 2, 3, 1
5) 3, 1, 2
6) 3, 2, 1

Now, since the table is circular, you will notice that there are repeating patterns. #1, #4, and #5 are the same. #2, #3, and #6 are the same. Therefore, there are really 2 combinations that are different = 2!.

 

[bpenly]

Sorry, I guess I explained it weird.

Try looking at this website

http://www.usask.ca/education/ideas/tplan/mathlp/a5.htm

It has a nice diagram.

In general, it is 6!/6 = 5! which then equals 120.

 

[boogaking]

OH!!!!!!!!!!!!!!!!!!!!!! AW!!!!!!!!!!!!!!!! This website proves useful once again... thanks all.... that website is pretty good...

 

[bpenly]

NO kidding. I had no idea how to do these problems about a week ago. Websites and peoples help on this forum are giving me a quick education on cute math tricks.