Transcript Warm-Up Exercises

Apply the Counting Principle
and Permutations
Section 10.1
Objectives:

Use the fundamental counting principle

Use permutations with and without
repetition
Key Vocabulary:
Permutation
 Factorial

Example 1:
A sporting goods store offers 3 types of
snowboards (all-mountain, freestyle, and
carving) and 2 types of boots (soft and
hybrid. How many choices does the
store offer for snowboarding equipment?
Fundamental Counting Principle
Example 2:
You are framing a picture. The frames are
available in 12 different styles. Each style
is available in 55 different colors. You
also want blue mat board, which is
available in 11 different shades of blue.
How many different ways can you frame
the picture?
Example 3:
The standard configuration for a Texas license plate is 1
letter followed by 2 digits followed by 3 letters.
a)
How many different license plates are possible if
letters and digits can be repeated?
b)
How many different license plates are possible if
letters and digits cannot be replaced?
#1: Complete.
The store in Example 1 also offers 3
different types of bicycles (mountain,
racing, and BMX) and 3 different wheel
sizes (20 in., 22 in., and 24 in.). How many
bicycle choices does the store offer?
#2: Complete.
In Example 3, how do the answers change
for the standard configuration of a New
York license place, which is 3 letters
followed by 4 numbers?
Permutations
A permutation is an arrangement of objects
in which order is important.
For instance, the 6 possible permutation of
the letters A, B, and C are shown:
ABC
ACB
BAC
BCA
CAB
CBA
Factorial
For any positive integer n, the product of
the integers from 1 to n is called n
factorial and it written as n!
The value of 0! Is defined to be 1.
Example 4:
Ten teams are competing in the final round of the
Olympic four-person bobsledding competition.
a) In how many different ways can the bobsledding
teams finish the competition? (Assume there are no
ties.)
b)
In how many different ways can 3 of the bobsledding
teams finish first, second, and third to win the gold,
silver, and bronze medals?
#3: Complete.
In Example 4, how would the answers
change if there were 12 bobsledding
teams competing in the final round of the
competition?
Permutations
Example 5:
You are burning a demo CD for your band.
Your band has 12 songs stored on your
computer. However, you want to put only
4 songs on the demo CD. In how many
orders can you burn 4 of the 12 songs
onto the CD?
#4: Find the number of
permutations.
5
P3
#5: Find the number of
permutations.
P
4 1
#6: Find the number of
permutations.
8
P5
#7: Find the number of
permutations.
12
P7
Permutations with Repetition
Example 6:
Find the number of distinguishable
permutation of the letters in
a)
MIAMI
b)
TALLAHASSEE
#8: Find the number of
distinguishable permutations of the
letters in the word.
MALL
#9: Find the number of
distinguishable permutations of the
letters in the word.
KAYAK
#10: Find the number of
distinguishable permutations of the
letters in the word.
CINCINNATI
Homework Assignment
Page 686 #4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28,
30, 32, 34, 36, 38, 40, 44, 46, 48, 50, 52, 54, 62, 66