A Permutation

There are n! ways to permute n objects. That means if I have 3 objects there are 3*2*1=6 ways that I can organize them in a line. If I have 8 objects, say people, and I want to put them in a line there are 8! = 40320 different ways. Now, if there are 8 books, numbered 1-8, and they are distributed to these 8 people and these 8 people sit down in a room in basically a semi-circle beginning at the door and following the wall around (there was a big TV on the other wall, hence the semi-circle) here are a few interesting stats-

There are 16 ways for the people to have sat in order 1 thru 8 beginning anywhere in the circle and going either direction around it. That makes a 1 in 2520 chance of that happening.

There are 2 ways for the people to have sat in order 1-8 beginning at either end of the semi-circle and going around the room (avoiding the break in the circle made by the tv). This makes a 1 in 20160 chance of that happening.

There is only one way for the 8 people to sit in order 1-8 beginning at the door and going around the semi-circle. A 1 in 40320 chance.

Guess what happened at the murder mystery last night...

P.S. It was a really fun evening. We did "The Wattersdown Affair." My character was an author who's murder mystery novels were praised for their incredible view into the mind of a murderer, naturally that means my character was in fact a murderer and had the audacity to write a "fictional" book based on it. Ha. In fact there were 2 characters who were confirmed murderers in the group and neither of us did it. In fact we were numbers 1 and 2 at the first. My friend Alycen has done 2 of these with me and each time her character has ended up being an American hussy. (We do not do that on purpose! You don't know until you get there all the dirt on your character) It was pretty funny. The game takes place in 1936 England, so we all got to dress up fancy and wear hats and talk with phony English accents. It was great! If I ever get a hold of some of the pictures I'll post them.