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GRE Math Challenge #12- Six people are asked to sit down in

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GRE Math Challenge #12- Six people are asked to sit down in [#permalink] New post 19 Sep 2014, 02:37
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Six people are asked to sit down in a circle consisting of eight chairs.How many different ways are there to distribute the six people on the eight chairs?

[Reveal] Spoiler: Answer
8!/ (8 * 2!) = 2,520

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Re: GRE Math Challenge #12- Six people are asked to sit down in [#permalink] New post 11 Sep 2017, 06:22
Please explain this. will b helpful, thanks
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Re: GRE Math Challenge #12- Six people are asked to sit down in [#permalink] New post 11 Sep 2017, 15:47
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sandy wrote:
Six people are asked to sit down in a circle consisting of eight chairs.How many different ways are there to distribute the six people on the eight chairs?

[Reveal] Spoiler: Answer
8!/ (8 * 2!) = 2,520


The basic idea here is that, for each possible arrangement, if EVERYONE moves 1 seat to the right, we have the same configuration.
Likewise, if EVERYONE moves 2 seats to the right, we have the same configuration.
Likewise, if EVERYONE moves 3 seats to the right, we have the same configuration.
.
.
.
Likewise, if EVERYONE moves 7 seats to the right, we have the same configuration.
So, one seating arrangement has 8 equivalent arrangements


At this point, let's NUMBER the 8 chairs as follows: #1, #2, #3, ..... #7 and #8
We'll call the six people A, B, C, D, E and F

Now seat each person.
We can place person A in one of 8 chairs
After that, we can place person B in one of the 7 remaining chairs
After that, we can place person C in one of the 6 remaining chairs
After that, we can place person D in one of the 5 remaining chairs
After that, we can place person E in one of the 4 remaining chairs
After that, we can place person F in one of the 3 remaining chairs

So, the number of arrangements = (8)(7)(6)(5)(4)(3)

HOWEVER, we're not quite done.
We have counted each equivalent seating 8 times
So, to account for this, we must divide (8)(7)(6)(5)(4)(3) by 8 to get: (8)(7)(6)(5)(4)(3)/8 = (7)(6)(5)(4)(3) = 2520

Cheers,
Brent
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Re: GRE Math Challenge #12- Six people are asked to sit down in   [#permalink] 11 Sep 2017, 15:47
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GRE Math Challenge #12- Six people are asked to sit down in

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