Question 1083527
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Saying <font color=blue>"8! is the answer"</font> is tempting, but it's incorrect. 


The actual answer is <font size=5 color=red>7!</font>. This is because there are 8 ways to rotate any given order, so we have {{{(8!)/8 = (8*7!)/8 = 7!}}}


You can think of it as setting one seat as the fixed seat. 
So we have 8-1 = 7 seats left to fill with 7 people. 
This is why you don't use the formula n! but instead (n-1)!


Check out these articles for further reading
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<li><a href = "https://www.dyclassroom.com/aptitude/circular-permutation">https://www.dyclassroom.com/aptitude/circular-permutation</a> (scroll down a bit past the middle)</li>
<li><a href = "https://math.illinoisstate.edu/day/courses/old/305/contentbasiccounting.html">https://math.illinoisstate.edu/day/courses/old/305/contentbasiccounting.html</a> (scroll down to around the bottom)</li>
<li><a href = "http://mathworld.wolfram.com/CircularPermutation.html">http://mathworld.wolfram.com/CircularPermutation.html</a></li>
</ul>
Your teacher made a typo when coming up with the answer choices. 
This is something you should talk to your teacher about.


For now the next best choice is choice C) 8! 
(which is what I'm assuming your teacher is probably going for, but as explained above, it's incorrect).
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