Permutations of Non-Distinguishable Objects

andCircular Permutations

Poker fun with your best friends by flickr user coltfan909

How many four-digit even numbers are there if the same digit cannot be used twice?

How many four-digit even numbers are there if the same digit can be repeated?

In how many ways can 8 books be arranged on a shelf, if 3 particular books must be together?

How many different 4 letter "words" can you make from the letters in the word BOOK?

B KOOB OO KBO K OBOK O

KO OBK O O BK O BOK OBO

Permutations of Non-Distinguishable Objects

The number of ways to arrange n objects that containsets of non-distinguishable objects is given by:

Example: How many different "words" can be made form the letters in the word:

# of O's = 2 ∴

# of I's = 4 # of S's = 4 # of P's = 2 ∴

(a) BOOK (b) MISSISSIPPI

How many different "words" can you make from the letters in the word STATISTICS?

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?

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

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

Circular Permutations

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

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