Circular permutations.

1. Circular Permutations
Circle of life

2. How many distinguishable ways can 3 people be seated around a
circular table?

4. How many distinguishable ways can 4 people be seated around a
circular table?

5. Circular Permutations
The number of ordered arrangements that can be made of n objects in a
circle is given by:
(n - 1)!
Example: How many different ways can 6 people be seated around a
circular table?
(6 - 1)! = 5!
= 120
Special Case: A bracelet is a circle that can be flipped over. The number of
different arrangements that can be made of objects on a bracelet is:
Example: How many bracelets can can be made from 6 different beads?
(6 - 1)! = 5!
2 2
= 60

6. How many distinguishable ways can 3 beads be arranged on a circular
bracelet?

7. How many distinguishable ways can 4 beads be arranged on a circular
bracelet?

8. In how many ways can 4 married couples seat themselves around a circular
table if:
(b) men and women alternate?
(a) spouses sit opposite each other?