At a certain dinner party, ten guests are to be seated around a circular table.?

Question

At a certain dinner party, ten guests are to be seated around a circular table. How many different arrangements are possidble? (Two arrangements are considered the same if each guest is seated between the same people.)

Answer 1

Oh good grief, let's eat.

Answer 2

The answer is 10! / 10.
10! or Ten factorial = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.
Picture the 10 people standing with all the chairs empty. The first person to sit has ten chair choices. The next person can fill one of the 9 remaining chairs, and so on.
There are, surprisingly, 3,628,800 different ways for those people to sit down. (10!)
HOWEVER: since the table is round, there are ten occurrences of each different arrangement. (After everyone sits down, they could rotate around the table in 10 different positions, but all of those are the same "arrangement."
So we divide the above number by 10, and there you have it.
362,880 different seating arrangements.
Bon appetit!

Answer 3

It will be 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2.

Once a person takes a seats there are 9 choices of who sits left of him. And then there are 8 choices for the seat left of this pair. And so on. The last person has only one seat left.

Answer 4

Sit them as man, woman, man, woman. Not necessarily with the woman or man they came with. Unless they request it before hand.

Answer 5

Make the people you don't like sit on a corner, or leave.

Answer 6

Is there going to be a test on this?

Answer 7

I'm with Will S.

....

ROTFLOL.


~Dark Aphotic

Answer 8

Is this another homework question?

Answer 9

I don't understand your last sentence.