EQ

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EQ

• When can we use the Counting Principles and how
  do they work?

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The possiblities are ENDLESS!

• How many locker combinations?
• How many license plates?
• How many phone numbers?
• How many routes to school from your house?
• How many passwords?

3
Count the Possibilities

• A deli has a lunch special which consists of a
  sandwich, a soup choice, and dessert for 4.99. 
  They offer the following choices
• Sandwich ham, and tuna, and roast beef
• Soup  tomato, chicken noodle
• Dessert cookie and pie
• How many different combinations of the lunch
  special are there?

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How did you organize your choices?
Sandwich Soup Dessert
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Tree Diagram
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How about the Counting Principle

• There are three stages in choosing a lunch special

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The Multiplication Principle of Counting

• Suppose a task involves a sequence of choices
• Divide the task into its different stages
• Determine how many ways each stage can occur
• Multiply the different number of ways each stage
  can occur

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You are taking a test that has five True/False
questions.  If you answer each question with True
or False and leave none of them blank, in how
many ways can you answer the whole test?
9
A company places a 6-symbol code on each unit of
product.  The code consists of 4 digits, the
first of which is the number 5,  followed by 2
letters, the first of which is NOT a vowel.  How
many different codes are possible?
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Work on problems with your partner.
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1. You are flipping a standard United States
quarter dollar. If you flip the quarter six
times and record the results (heads or tails for
each flip), how many possible ways could your
results be recorded when you finish all six
events? (example one way could be H,T,H,H,T,
and H. There are several other possible results
for the six events of flipping a quarter. How
many are there?)
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2. Magdalena has 6 hats, 2 scarves and 5 pairs
of mittens. In how many different ways can she
wear a hat, a scarf and a pair of mittens?
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3. How many different license plates can be
formed that are made up of 3 numbers followed by
3 letters?
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4. Six students in a speech class all have to
give there speech on the same day.  One of the
students insists on being first.  If this
students request is granted, how many different
ways are there to schedule the speeches?
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5. How many different 5 character stock numbers
can be formed if the first digit cannot be zero,
the second digit must be odd and the last three
digits are alphabetic?
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The Addition Principle of Counting

• Suppose the possibilities being counted can be
  divided into groups with no possibilities in
  common
• 1) Determine how many groups of possibilities
  there are.
• 2) Count the number of possibilities within each
  group.
• 3) Add the number of possibilities within each
  group.

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Count the Possibilities

• A deli has a lunch special which consists of
  either a sandwich or soup for 2.00.  They offer
  the following choices
• Sandwich ham, and tuna, roast beef, turkey
• Soup  tomato, chicken noodle, vegetable
• How many lunch specials are there?

18
A Night Out

• Four friends are planning next Friday night. So
  far it has been decided that they will begin the
  evening by eating at a Mexican, Chinese, or
  Italian restaurant. Then, they are going to go
  see one of the 5 movies that start around 800 at
  the local cinema. Afterwards, they will be
  spending the night at one of the friends home.
  How many possible outcomes are there for Friday
  night?
• Four friends are planning next Friday night. So
  far it has been decided that they will either eat
  at a Mexican, Chinese, or Italian restaurant, go
  to see one of the 5 movies that start around 800
  at the local cinema, or spend the night at one of
  the friends home. How many possible outcomes are
  there for Friday night?

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How many different iPods can you choose?
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Each student at a certain school is assigned an
identification card that contains a unique 4
character/symbol (letter or digit) barcode. Each
barcode contains either one or zero digits. How
many unique id cards are possible?
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Work on Problems with your partner.
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1. TJ is choosing an elective for his
first-period class. He can choose from 3
different art classes, 4 different world language
classes and 2 different computer classes. How
many different possible selections could TJ make
for his first period elective?
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2. A Chinese restaurant serves 25 rice dishes
and 10 noodle dishes. If Simon orders either a
rice dish or a noodle dish, from how many dishes
can he chose?
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3. Majestic Cinemas is showing 7 comedy movies
today and MCT Cinemas is showing 5 action movies.
If Juliette will see either a comedy at Majestic
Cinemas or an action move at MCT Cinemas, how
many different movie selections could she make?
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• 4. The password for a websites login must have
  exactly 5 characters. The characters must be a
  digit or a letter. Each password can have one or
  zero letters.
• How many possible passwords could be
  generated with this criteria?

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5. A schools locker combinations consist of a
3 symbol code (letters and digits). If there is
a maximum of one letter in each combination, how
many combinations are possible?
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• 6. You are the coach of a little league baseball
  team and youre buying trophies for the end of
  the season banquet. Each player on the team
  will receive trophy. Each trophy can be engraved
  with the players full name, first name only, or
  a nickname, and the defensive position the player
  played most often (There are nine defensive
  positions in baseball.). How many different
  engravings are possible if the defensive position
  can be the first or last part of the engraving on
  a trophy?