EQ
When can we use the
Counting Principles and
how do they work?
“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?
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?
How did you organize your
choices?
Sandwich Soup Dessert
Tree Diagram
How about the Counting
Principle
There are three stages in choosing a
lunch special
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
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?
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?
Work on problems with your
partner.
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.
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?
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 8:00 at the local cinema. Afterwards, they
will be spending the night at one of the friend’s 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 8:00 at the local cinema, or
spend the night at one of the friend’s home. How many
possible outcomes are there for Friday night?
How many different iPods can
you choose?
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?
Work on Problems with your
partner.
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?
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?
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?
4. The password for a website’s 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?
5. A school’s 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?
6. You are the coach of a little league baseball team and
you’re buying trophies for the end of the season
banquet. Each player on the team will receive trophy.
Each trophy can be engraved with the player’s 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?