Circular Permutations

Circle of life

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

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

(6 - 1)! = 5! 2 2 = 60

Example: How many bracelets can can be made from 6 different beads?

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:

(6 - 1)! = 5! = 120

Example: How many different ways can 6 people be seated around a circular table?

(n - 1)!

The number of ordered arrangements that can be made of n objects in a circle is given by:

Circular Permutations

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

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

(b) men and women alternate?(a) spouses sit opposite each other?

In how many ways can 4 married couples seat themselves around a circular table if: