CIRCLE PERMUTATIONS

* formula: (n-1)!

EX 1. There are tem people. How many permutations are there for them to sit around a table?

(n-1)! = (10-1)!
= 9!
= 362 880


EX 2. Lorena and Caroline must sit together. (They are able to switch around in order)

The table alos must seat: Jackie, Jennifer, and Eddie...

n=4
(n-1)! = 3!
= 3! * 2!
= 12 ways

EX 3. Now, we have Lorena + Carloine and Jackie + Jennifer who must sit together, leaving Eddie all lone.


* Eddie and the pair of two girls are considered to be represented by 2!

n=3 -> (n-1)!=2!
=2!
=2!
= 2! * 2! * 2! = 8 ways


EX 4. Lastly, Lorena and Caroline don't want to be near each other.

(5-1)!=4!

* You aren't done yet. This equation will help solve for this specific problem:

total - together = not together
= 24-12 =12


I love Regine is the next scribe!