Simple Algebra equations , math homework help

Please complete the following questions. It is important that you show all work you did to solve the problems when you submit your work. This includes any calculations, diagrams, or graphs that helped you solve it.

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.Find pages 684 and 710 attached.

12-1
The Counting Principle
Main Ideas
DAN FLORIDA 99
• Solve problems
involving independent
events.
Solve problems
involving dependent
events.
GET READY for the Lesson
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
New Vocabulary
outcome
sample space
event
independent events
Fundamental Counting
Principle
dependent events
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 lail.
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 nol 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
H
С
F.
Bun
Р
S
P
S
Р
S
Reading Math
There are both infinite
and finite sample spaces.
Finite sample spaces have
a countable number of
possible outcomes, such
as rolling a die. Infinite
sample spaces have an
uncountable number of
possible outcomes, such
as the probability of a
point on a line.
Possible Combinations HP HS CP CS FP FS
Method 2 Make a Table
Bun
Make a table in which cach row
Plain Sesame
represents a type of meat and each
Hamburger HP HS
columnn represents a type of bun.
Meal Chicken CP CS
There are six possible outcomes.
Fish
FP FS
CHECK Your Progress
1. A cafeteria offers drink choices of water, coffee, juice, and milk and
salad choices of pasta, fruit, and potato. How many different
combinations of drink and salad are possible?
12-2
Permutations and
Combinations
Main Ideas
Solve problems
involving
permutations.
• Solve problems
involving
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.
New Vocabulary
permutation
linear permutation
combination
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!.
7.6.5.4 = 7.6.5.4.
3.2.1
3.2.1
Multiply by
3.2.1
3.2.1
or 1.
7.6.5.4.3.2.1
or
3.2.1
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
Reading Math
KEY CONCEPT
Permutations
The number of permutations of n distinct objects taken at a time is given by
P(n,r) =
(n-1)!
n!
Permutations The
expression Pin, n) reads
the number of
permutations of n
objects taken r at a
time. It is sometimes
written as P
EXAMPLE
Permutation
FIGURE SKATING There are 10 finalists in a figure skating competition.
How many ways can gold, silver, and bronze medals be awarded?
Since each winner will receive a different medal, order is important. You
must find the number of permutations of 10 things taken 3 at a time.