Discrete Mathematics
# Permutations

The mathematician, physicist, engineer, and computer scientist decide to move from the bar to a (circular) table. They file to the table, **staying in order** as they sit down and wind up seated as shown below.

How many different seating arrangements at the bar will lead to the seating arrangement around the table in the image above?

**Assumptions and details:**

"Staying in order" means that each person has the same left and right neighbors that they had at the bar (though the person who was sitting on the left end at the bar will now be sitting to the right of the person who was sitting on the right end at the bar).