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In how many different ways (relative to each other) can 8

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In how many different ways (relative to each other) can 8 [#permalink] New post 28 Feb 2013, 11:24
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In how many different ways (relative to each other) can 8 friends sit around a square table with 2 seats on each side of the table?

OA:
[Reveal] Spoiler:
2*7!
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Re: In how many different ways (relative to each other) can 8 [#permalink] New post 28 Feb 2013, 12:44
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Normally the formula for items in a circle is (n-1)! - in this case this is the 7!

It is multiplied by 2 because of the rest of the information. If you have the same arrangement of people you can have everyone shift one position to the right (or left) and they will be sitting next to a different person. With 2 shifts they will be back to sitting next to the original person.

Hope this helps.
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Re: In how many different ways (relative to each other) can 8 [#permalink] New post 24 Jun 2015, 10:47
In how many different ways (relative to each other) can 8 friends sit around a square table with 2 seats on each side of the table?

A) 2 * 8!
B) 2 * 7!
C) \(\frac{8!}{4!}\)
D) (8-1)!
E) 8!/2
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Re: In how many different ways (relative to each other) can 8 [#permalink] New post 24 Jun 2015, 10:49
Please help me with understanding the OA and why it is not
[Reveal] Spoiler: option
D?

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Re: In how many different ways (relative to each other) can 8 [#permalink] New post 24 Jun 2015, 17:48
Patronus wrote:
In how many different ways (relative to each other) can 8 friends sit around a square table with 2 seats on each side of the table?

A) 2 * 8!
B) 2 * 7!
C) \(\frac{8!}{4!}\)
D) (8-1)!
E) 8!/2


Hi,
We can take this square as a circle but with one difference....
first, if it were a circle , the ways would be 7!..
now only difference is in each arrangement of 7!, any particular person would be sitting with two different person on an edge of the table
that is he would be sitting with the person on his left on one side of the square and with the one on his right in the next arrangement without shifting relatively to each other..
so we multiply each arrangement with 2.. ans 7!*2
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Re: In how many different ways (relative to each other) can 8 [#permalink] New post 24 Jun 2015, 20:13
Expert's post
mun23 wrote:
In how many different ways (relative to each other) can 8 friends sit around a square table with 2 seats on each side of the table?
answer is 2*7!
need the explanation..........I an not understanding how to solve


I gave the solution to this problem in the post after the post on circular arrangements:
http://www.veritasprep.com/blog/2011/10 ... ts-part-i/

The answer is 2*7!
It's explained in detail on the link given above.
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Re: In how many different ways (relative to each other) can 8 [#permalink] New post 25 Jun 2015, 03:08
I am not sure I understand this comopletely.

For me, all 8 seats for the first person are the same. But, if he sits on seat 1, then there are 7! remaining ways for the other people to be seated. If he seats on seat 2 (the other corner of that same side of the table) then there are 7! remaining ways for the rest of the people to be seated. The difference is that person one will be next to another person depending on which seat he chooses to sit on.

So, in this sense, 2*7! makes sense.

But, I don't get why 2-4-6-8 seats are the same and 1-3-5-7 similarly the same, creating the *2 in the response.
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Re: In how many different ways (relative to each other) can 8 [#permalink] New post 25 Jun 2015, 03:18
pacifist85 wrote:
I am not sure I understand this comopletely.

For me, all 8 seats for the first person are the same. But, if he sits on seat 1, then there are 7! remaining ways for the other people to be seated. If he seats on seat 2 (the other corner of that same side of the table) then there are 7! remaining ways for the rest of the people to be seated. The difference is that person one will be next to another person depending on which seat he chooses to sit on.

So, in this sense, 2*7! makes sense.

But, I don't get why 2-4-6-8 seats are the same and 1-3-5-7 similarly the same, creating the *2 in the response.



OK... I just realised that the first person choosing seat 1 or 2 , and generally choosing 1-3-5-7 or 2-4-6-8 is actually exactly the same thing...
Re: In how many different ways (relative to each other) can 8   [#permalink] 25 Jun 2015, 03:18
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