According to a math website I'm looking at (http://web.eecs.utk.edu/~booth/311-04/notes/combinatorics.html), if you have a circular permutation situation (such as a round table), and there are e empty spaces, then the formula is…
(n-1)! / e!
However this doesn't make complete sense to me. Say for instance, I want to seat 3 people at a table with 30 seats. That means there will be 27 empty seats. So total number of ways to seat them is…
(3-1)! / 27! = (extremely below 0)
Can someone explain how my thinking on this is wrong? It would be greatly appreciated!
Best Answer
n is the number of seats; not the number of people.
Thus number of ways to seat 3 people in 30 seats is (30 -1)!/27! = 29*28.
(I'm assuming that the point of the table being circular is that seatings are equivalent up to rotation. Thus when the first person sits all choices are considered equivalent.)