Fundamental Counting Principle

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Fundamental Counting Principle
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TOTAL OF OUTCOMES EX. School uniforms How
many different outcomes can you make with three
different shirts and two pairs of pants? 3 X 2
6 different outfits
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Example 1 A
License plates are being produced that have a
single letter followed by three digits. All
license plates are equally likely.
Find the number of possible license plates.
Use the Fundamental Counting Principal.
second digit
letter
first digit
third digit
26 choices
10 choices
10 choices
10 choices
26 10 10 10 26,000
The number of possible 1-letter, 3-digit license
plates is 26,000.
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Example 1 B
Find the probability that a license plate has the
letter Q.
0.038
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Example 1 C
Find the probability that a license plate does
not contain a 3.
First use the Fundamental Counting Principle to
find the number of license plates that do not
contain a 3.
26 9 9 9 18,954 possible license plates

without a 3
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The Fundamental Counting Principle tells you only
the number of outcomes in some experiments, not
what the outcomes are. A tree diagram is a way to
show all of the possible outcomes.
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Example 2
You have a photo that you want to mat and frame.
You can choose from a blue, purple, red, or green
mat and a metal or wood frame. Describe all of
the ways you could frame this photo with one mat
and one frame.
You can find all of the possible outcomes by
making a tree diagram.
There should be 4 2 8 different ways to frame
the photo.
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Example 2
Each branch of the tree diagram represents a
different way to frame the photo. The ways shown
in the branches could be written as (blue,
metal), (blue, wood), (purple, metal), (purple,
wood), (red, metal), (red, wood), (green, metal),
and (green, wood).
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On your own
Flip your paper over and do this on the back
A baker can make yellow or white cakes with a
choice of chocolate, strawberry, or vanilla
icing. Describe all of the possible combinations
of cakes.
You can find all of the possible outcomes by
making a tree diagram. There should be 2 3 6
different cakes available.
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Does your paper look something like this?
yellow cake
The different cake possibilities are (yellow,
chocolate), (yellow, strawberry), (yellow,
vanilla), (white, chocolate), (white,
strawberry), and (white, vanilla).
vanilla icing
chocolate icing
strawberry icing
white cake
vanilla icing
chocolate icing
strawberry icing
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Addition Counting Principle
The table shows the items available at a farm
stand. How many items can you choose from the
farm stand?
Apples Pears Squash
Macintosh Bosc Acorn
Red Delicious Yellow Bartlett Hubbard
Gold Delicious Red Bartlett
None of the lists contains identical items, so
use the Addition Counting Principle.
Total Choices 8
Apples 3
Pears 3
Squash 2



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Addition Counting Principle vs. Fundamental
Counting Principle
Addition Counting Principle shows the number of
options or choices Fundamental Counting
Principle shows all possible combinations
(outcomes)