12.1 SPECIAL TYPES OF PERMUTATIONS
Introductory Activity:
Students break into groups of four and five. Students should figure out how
many ways they can arrange themselves in a circle.
Take the values attained by each group to come up with a general formula
for a “circular permutation.”
CIRCULAR PERMUTATION: How many ways can you arrange
n objects in a circle ?
Example: A disc jockey is setting up some of the music she will be
playing during her shift. She is loading a CD tray with
six different CDs. How many different ways can these
discs be arranged on the circular tray ?
Circular Permutation with a Fixed Point
Example: An empty circular cul-de-sac is ready to be developed into
five different lots with each having a different home design.
There is one opening to the cul-de-sac. How many arrangements
of the homes are possible ?
12.1 SPECIAL TYPES OF PERMUTATIONS
How many distinguishable permutations are in the word MOM ?
How many distinguishable permutations are in the word OHIO ?
PERMUTATIONS WITH REPETITIONS: The number of distinguishable
permutations of n objects where one object is repeated q1 times,
another is repeated q 2 times and so on is :
n!
q1!⋅ q 2 ! ⋅ L ⋅ q k !
Example: Find the number of distinguishable permutations of the word
MISSISSIPPI