SOLUTION: the number of ways that 8 people could be seated around the table would be computed from 8 to the 8th power 8*8 8! 8!/4!4!

Question 1083527: the number of ways that 8 people could be seated around the table would be computed from

8 to the 8th power

8*8

8!

8!/4!4!

Found 2 solutions by addingup, jim_thompson5910:
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
8, seat 1. Now you have 7, seat another one. Now you have 6. Etcetera.
8*7*6*5*4*3*2*1 or in factorial form: 8!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Saying "8! is the answer" is tempting, but it's incorrect.

The actual answer is 7!. This is because there are 8 ways to rotate any given order, so we have

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

https://www.dyclassroom.com/aptitude/circular-permutation (scroll down a bit past the middle)

https://math.illinoisstate.edu/day/courses/old/305/contentbasiccounting.html (scroll down to around the bottom)

http://mathworld.wolfram.com/CircularPermutation.html

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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