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.
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.
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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