1

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!

user2779949
  • 117
  • Nitpick. 2!/27! is not below zero. But it is "extremely" fractional and clearly not a non-negative integer which "the number of ways" has to be. – fleablood Nov 12 '15 at 20:09
  • By the way, I did not particularly like that page you linked to. I thought the explanations were poorly worded and confusing. – fleablood Nov 12 '15 at 20:14

1 Answers1

1

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.)

fleablood
  • 124,253