Geometry & Finite H
Mr. Russo
Name: _______________________
Date: _______________________
Circular Permutations & Repetitions
Circular Permutation: An arrangement of objects in a specific order, where the last object is next to the 1st one
(…like around a circle).
How many ways can 4 people sit around a table, relative to each other? Here’s 1 way:
A
D
B
C
Draw other ways until you have them all. (We’ll do this together on the board.) Be sure you don’t repeat any!

We already know: number of ways to arrange n things in a row = n Pn = ________

Now, we also know: number of ways to arrange n things around something = __________ (circular!)
This time, n = ____, so there are __________ = ______ = ______ ways to arrange 4 people around a table.
Repetitions…
Make a list of all the arrangements of the letters in:
YES
NON
MOON
NOON
NOOO
You may notice that a repeated letter (or letters) means fewer arrangements. (Oh yeah, I noticed.)

Number of ways to arrange n different things in a row = _____

Number of ways to arrange n things in a row when 1
is repeated p times and another is repeated q times =
How many ways can you arrange the letters in MISSISSIPPI?
A few chumpies to try:
1.) Find the number of permutations of six colors on a spinner.
2.) Find the number of permutations (arrangements) of the letters of these words:
a.) DEED
b.) COMMITTEE
c.) CINCINNATI
3.) A player in a word game has the letters E,E,B,D,G,G,G. In how many ways can these letters be arranged?
4.) In how many ways can 4 blue, 3 red, and 2 green flags be arranged on a pole?
5.) Find the number of ways 10 cheerleaders can make a circular formation.
Answers!
1.) (6 – 1)! = 5! = 120
3.)
7!
 420
3!2!
!
24

6
2!2! 4
9!
 1260
4.)
4!3!2!
2a.)
2b.)
9!
 45,360
2!2!2!
2c.)
10!
 50, 400
3!3!2!
5.) (10  1)!  9!  362,880
_________________________________________________________________________________________
Ponder the following: A keychain has 3 keys (1 red, 1 green, and 1 blue). Here’s one arrangement for the keys:
Draw all other arrangements for the keys. Be sure you don’t repeat any!
HW 6
 This means that there is a group of 3
people that must sit together.
13.) Tom, Susie, Marilyn, Joe, Erica, Tori, Meredith and Derek are taking water skiing lessons. In how many
ways could they line up if:
a) there are no special conditions (i.e., anyone can be anywhere in the line)?
b) all of the boys will go first?
c) Erica wants to go right before Derek?
d) Joe and Marilyn want to be beside each other but don’t care which order?
e) Tori does not want to go first and Joe does not want to go last?
f) Tom and Susie do NOT want to be beside each other?
g) the whole group is standing in a circle rather than a line?
h) in the line, Erica, Tori and Meredith want to all be beside each other, in any order?