MATH125 AIU Counting Techniques and Probability Paper All questions have to be answered and show all step by step calculations. Text book used is General College Math by editorial board, Words of Wisdom. NAME:

MATH125: Unit 8 Submission Assignment Answer Form

Counting Techniques

ALL questions below must be answered. Show ALL step-by-step calculation. Upload this modified

Answer Form to the intellipath Unit 8 Submission lesson. Make sure you submit your work in a modified

MS Word document; handwritten work will not be accepted. If you need assistance, please contact your

course instructor.

Part A: Combinations and Permutations

1. Differentiate between permutations and combinations. How are they different? What is the

formula for each? (15 points total for Question 1)

How are they different?

(5 points)

?

Permutation Formula

(5 points)

?

Combination Formula

(5 points)

?

2. Each state has a standard format for license plates that includes a set number of alphanumeric

characters. For this assignment, you can insert a picture of your states non-personalized license

plate or provide a sample of the format in text. (20 points total for Question 2)

Your States Name

(1 point)

Picture of a License Plate

from Your State

(or a Sample)

(1 point)

?

?

Describe the Character

Rule for Your States

Non-personalized

License Plates

(1 point)

?

a. Determine the number of different license plates that can be created using the

following format. Assume that a license plate consists of seven alphanumeric characters

using numbers (09) and capital letters (AZ). Find how many unique license plates can

be printed using any of the 36 alphanumeric characters without duplication in each of

the seven alphanumeric characters, i.e., no alphanumeric character appears more than

once in any license plate. (This question is NOT related to your states license plates in

the initial 3 parts above).

Is this a permutation or

combination? Why?

(2 points)

What formula from

Question 1 will you use

to solve the problem?

(1 point)

Number of unique

license plates that can be

printed:

(2 points)

?

?

?

Show your work here (2 points):

b. You and a friend are witnesses of a car accident in your state. But you can only

remember a few of the first alphanumeric characters on the license plate.

How many alphanumeric

characters do you

remember?

(1 point)

?

(Select a number from 2 to 5)

What are the characters

at the beginning?

(1 point)

?

How many license plates

start with these

alphanumeric

characters?

(2 points)

?

Show your work here (2 points):

How many license plates

have been eliminated?

(2 points)

?

Show your work (2 points):

3. Your community has asked you to help the YMCA sports director organize a season of sports.

You need to put together the teams. For the soccer teams, athletes signed up for one of three

different age groups (Little Tykes, Big Kids, and Teens). (15 points total for Question 3)

Is this a permutation or

combination? Why?

(2 points)

?

What formula from

Question 1 will you use

to solve the problem?

(1 point)

?

How many kids signed

up for Little Tykes?

(1 point)

How many kids signed

up for Big Kids?

(1 point)

?

(Select a multiple of 10, of at least 20)

?

(Select a multiple of 10, of at least 20)

How many kids signed

up for Teens?

(1 point)

How many total

students signed up for

soccer?

(1 point)

?

(Select a multiple of 10, of at least 20)

?

(enter total form the three groups above)

Use the formula and values, from question above, to answer the following:

How many different

ways can you create

teams of 10 for the

Little Tykes grade

level?

(2 points)

?

Show your work here: (2 points)

If age levels did not

matter, how many

different ways can you

create teams of 10 from

?

the total number of

soccer players?

(2 points)

Show your work here: (2 points)

Part B: Probabilities and Odds

4. For this set of exercises, you will need a single standard six-sided die. If you do not have one,

you can use a virtual die: https://www.random.org/dice/ (40 points total for Question 4)

a. First, differentiate between odds and probability.

How are odds

and probability

different?

(2 points)

What is the

odds in favor

ratio?

(3 points)

What is the

probability of

an event ratio?

(3 points)

?

?

?

?

What are the odds of

rolling a three (use the

proper ratio from above)?

Simplify all fraction

answers.

(2 points)

What is the theoretical

probability of rolling a

three (use the proper

ratio from above)?

Simplify all fraction

answers.

(2 points)

?

b. Reflect on the previous questions answer outcome. First, convert the fraction to a

percent.

Percent Probability

Theoretical Probability

(Rounded to the nearest

whole percent.)

(2 points)

?

Next, use the likelihood scale table above to select the term that best describes your answer.

Likelihood Scale

Term

(2 points)

?

c. What if someone challenged you to never roll a 3? If you were to roll your single sixsided die 18 times, what would be the empirical probability of never getting a three?

Also, list the likelihood scale term from the table above.

Percent Probability

Solution

(Rounded to the

Nearest Whole Percent)

(2 points)

Likelihood Scale Term

(2 points)

?

?

Show your work here: (2 points)

d. After 18 rolls, what would be the empirical probability of getting a three on at least one

of those rolls? Also, list the likelihood scale term from the table above.

Percent Probability

Empirical Probability

(Rounded to the

Nearest Whole Percent)

(2 points)

Likelihood Scale Term

(2 points)

?

?

Show your work: (2 points)

What do you notice

about the answers for

parts c and d above?

(2 points)

?

e. Roll the die 18 times and keep track of what is rolled in the table below. Remember, if

you do not have one, you can use virtual dice: https://www.random.org/dice/ (2 points)

Roll #

Roll 1

Roll 2

Roll 3

Roll 4

Roll 5

Roll 6

f.

Dice

Roll #

Dice

Roll #

Dice

?

Roll 7

?

Roll 13

?

?

Roll 8

?

Roll 14

?

?

Roll 9

?

Roll 15

?

?

Roll 10

?

Roll 16

?

?

Roll 11

?

Roll 17

?

?

Roll 12

?

Roll 18

?

Based on your die rolls, what is the experimental probability of rolling a three, out of 18

rolls? Also, list the likelihood scale term from the table above.

Percent Probability

Experimental Probability

(Rounded to the Nearest

Whole Percent)

(2 points)

Likelihood Scale Term

(2 points)

?

?

Show your work here: (2 points)

With regard to the

likelihood scale terms

for each, how did this

differ from both the

theoretical and empirical

probabilities?

(2 points)

?

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