Applications of Probability Describe a situation in which the number of outcomes is given by P(6, 3).

1. OPEN ENDED Describe a situation in which the number of outcomes is given by P(6, 3).
2. OPEN ENDED Describe an event that has a probability of 0 and an event that has a probability of 1.
3. Writing in Math Use the information on page 684 to explain how you can count the maximum number of license plates a state can issue. Explain how to use the Fundamental Counting Principle to find the number of different license plates in a state such as Oklahoma, which has 3 letters followed by 3 numbers. Also explain how a state can increase the number of possible plates Without increasing the length of the plate number.
4. Writing in Math Use the information on page 710 to explain how permutations and combinations apply to softball. Explain how to find the number of 9-person lineups that are possible and how many ways there are to choose 9 players if 16 players show up for a game.

GET READY for the Lesson
JAN TORIDA 1992
The number of possible license
plates for a state is too great to
count by listing all of the
possibilities. It is much more
efficient to count the number of
possibilities by using the
Fundamental Counting Principle.
XXF 466
BROWARD
Independent Events An outcome is the result of a single trial. For
example, the trial of flipping a coin once has two outcomes: head or tail.
The set of all possible outcomes is called the sample space. An event
consists of one or more outcomes of a trial. The choices of letters and
digits to be put on a license plate are called independent events because
each letter or digit chosen does not affect the choices for the others.
EXAMPLE
Independent Events
FOOD A sandwich cart offers customers a choice of hamburger,
chicken, or fish on either a plain or a sesame seed bun. How many
different combinations of meat and a bun are possible?
First, note that the choice of the type of meat does not affect the choice
of the type of bun, so these events are independent.
Method 1 Tree Diagram
H represents hamburger, C, chicken, F, fish, P, plain, and S, sesame seed.
Meat
Н
F
Bun
P
S
S
|
HS
P
1
CP
S
.
CS
P
1
FP
HP
Possible Combinations
Method Maken tulo
FS
Permutations and
Combinations
GET READY for the Lesson
When the manager of a softball team fills
out her team’s lineup card before the game,
the order in which she fills in the names is
important because it determines the order
in which the players will bat.
Suppose she has 7 possible players in mind
for the top 4 spots in the lineup. You know
from the Fundamental Counting Principle
that there are 7.6.5.4 or 840 ways that
she could assign players to the top 4 spots.
Permutations When a group of objects or people are arranged in a
certain order, the arrangement is called a permutation. In a permutation,
the order of the objects is very important. The arrangement of objects or
people in a line is called a linear permutation.
Notice that 7.6.5.4 is the product of the first 4 factors of 7!. You can
rewrite this product in terms of 7!.
3.2.1
7.6.5.4=7.6.5.4.
3.2.1
Multiply by:2:1 or 1.
2:
7.6.5.4.3.2.1
3.2.1
or 7
7!
or
7!=7.6.5.4.3.2.1 and 3!= 3.2.1
Notice that 3! is the same as (7 – 4)!
The number of ways to arrange 7 people or objects taken 4 at a time is
written P(7,4). The expression for the softball lineup above is a case of
the following formula.
h
KEY CONCEPT
Permutations
The number of permutations of n distinct objects taken r at a time is given by
n!
P(n,n) =
(n.
மைகள்
16,532
SEP
20