The counting principle

1. The
Counting
Principle

2. Counting Outcomes
Have you ever seen or heard the
Subway or Starbucks advertising
campaigns where they talk about the
10,000 different combinations of ways
to order a sub or drink?

3. Counting Outcomes
Have you ever seen or heard the
Subway or Starbucks advertising
campaigns where they talk about the
10,000 different combinations of ways
to order a sub or drink?
When companies like these make
these claims they are using all the
different condiments and ways to
serve a drink.

4. Counting Outcomes
- These companies can use (2) ideas
related to combinations to make these
claims:
(1) TREE DIAGRAMS
(2) THE FUNDAMENTAL
COUNTING PRINCIPLE

5. Counting Outcomes
(1) TREE DIAGRAMS
A tree diagram is a diagram used to show
the total number of possible outcomes in
a probability experiment.

6. Counting Outcomes
(2) THE COUNTING PRINCIPLE
The Counting Principle uses multiplication of
the number of ways each event in an
experiment can occur to find the number
of possible outcomes in a sample space.
http://www.youtube.com/watch?v=8WdSJh
EIrQk&safe=active

7. Counting Outcomes
Example 1: Tree Diagrams.
A new polo shirt is released in 4 different
colors and 5 different sizes. How many
different color and size combinations are
available to the public?
Colors – (Red, Blue, Green, Yellow)
Styles – (S, M, L, XL, XXL)

8. The Tree Diagram

9. A Different Way
Example 1: The Counting Principle.
A new polo shirt is released in 4 different
colors and 5 different sizes. How many
different color and size combinations are
available to the public?
Colors – (Red, Blue, Green, Yellow)
Styles – (S, M, L, XL, XXL)

10. Counting Outcomes
Example 1: The Fundamental Counting
Principle.
Answer.
Number of Number of Number of
Possible Styles Possible Sizes Possible Comb.
4 x 5 = 20

11. Counting Outcomes
 Tree Diagrams and The Fundamental
Counting Principle are two different
algorithms for finding sample space of
a probability problem.
 However, tree diagrams work better
for some problems and the
fundamental counting principle works
better for other problems.

12. So when should I use a tree diagram or
the fundamental counting principle?
- A tree diagram is used to:
(1) show sample space;
(2) count the number of preferred outcomes.
- The fundamental counting principle can
be used to:
(1) count the total number of outcomes.

13. Counting Outcomes
Example 2: Tree Diagram.
Tamara spins a spinner two
times. What is her probability
of spinning a green on the
first spin and a blue on the second spin?
You use a tree diagram because you want a
specific outcome … not the TOTAL
number of outcomes.

14. Counting Outcomes
Example 2: Tree Diagram.
Tamara spins a spinner two
times. What is her probability
of spinning a green on the
first spin and a blue on the second spin?

15. Counting Outcomes
Example 3: The Counting Principle.
If a lottery game is made up of three
digits from 0 to 9, what is the total
number of outcomes?
You use the Counting Principle because you
want the total number of outcomes. How
many possible digits are from 0 to 9?

16. Counting Outcomes
Example 3: The Fundamental Counting
Principle.
If a lottery game is made up of three digits
from 0 to 9, what is the total number of
possible outcomes?
# of Possible # of Possible # of Possible # of Possible
Digits Digits Digits Outcomes
10 x 10 x 10 = 1000
What chance would you have to win if you played one time?

17. Guided Practice: Tree or Counting
Principle?
(1) How many outfits are possible from a pair
of jean or khaki shorts and a choice of
yellow, white, or blue shirt?
(2) Scott has 5 shirts, 3 pairs of pants, and 4
pairs of socks. How many different outfits
can Scott choose with a shirt, pair of
pants, and pair of socks?

18. Example 1
 You are purchasing a new car. Using the
following manufacturers, car sizes and colors,
how many different ways can you select one
manufacturer, one car size and one color?
Manufacturer: Ford, GM, Chrysler
Car size: small, medium
Color: white(W), red(R), black(B), green(G)

19. Solution
 There are three choices of manufacturer, two
choices of car sizes, and four colors. So, the
number of ways to select one manufacturer, one
car size and one color is:
3 ●2●4 = 24 ways.

20. Ex. 2 Using the Fundamental Counting
Principle
 The access code for a car’s security system
consists of four digits. Each digit can be 0
through 9. How many access codes are possible
if each digit can be repeated?