Differentiate between permutations and combinations. How are they different? What is the formula for each?

  
MATH125: Unit 4 Submission Assignment Answer Form
Counting Techniques and Introduction to Probability
ALL questions below must be answered. Show ALL step-by-step calculation. Upload this modified Answer Form to the intellipath Unit 4 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 & Permutations
1. Differentiate between permutations and combinations. How are they different? What is the formula for each? (15 points)
  
How are they different?
(5 pts)

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Permutation Formula
(5 pts)

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Combination Formula
(5 pts)

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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 state’s non-personalized license plate or provide a sample of the format in text. (20 points total for Question 2)
  
Your State’s Name
(1 pt)

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Picture of a License Plate from Your   State
(Or a Sample)
(1 pt)

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Describe the rule for your state’s non-personalized license plates.
(1 pt)

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a. Determine the number of different license plates that can be created using this format. Assume that a license plate consists of seven alphanumeric characters using numbers (0-9) and capital letters (A-Z). Find how many unique license plates can be printed using all alphanumeric characters only once.  
  
Is   this a permutation or combination? Why?
(2   pts)

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What   formula from #1 above will you use to solve the problem?
(1   pt)

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Solution:
(4   pts)

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Show your work: 
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 pt)

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(Select a number from 2 to 5)
  
What are the characters at the beginning?
(1 pt)


  
How many license   plates start with these alphanumeric characters?
  (4 pts) 

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Show your work: 
  
How many license plates have been   eliminated?
(4 pts)

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Show your work: 
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 with three different age groups. How many different ways can you organize teams of ten for each age group? (15 points)
  
Are these a permutation or combination? Why?
(2 pt)

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What formula from #1 above will you use   to solve the problem?
(1 pt)

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How many students signed up for soccer?
(1 pt)

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(Select a multiple of 10, from 30 to 100)
  
How many kids signed up for “Little Tykes”   under the age of seven?
(1 pt)

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(Select a multiple of 10, of at least 20)
  
How many kids signed up for “Big Kids”   between 8 and 12?
(1 pt)

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(Select a multiple of 10, of at least 20)
  
How many kids signed up for “Teens”   between 13 and 18?
(1 pt)

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(Select a multiple of 10, of at least 20)
  
How many different ways can you create   teams of ten for the “Little Tykes” grade level?
(2 pts)

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Show your work: (2 pts)
  
If age levels did not matter, how many   different ways can you create teams of ten?
(2 pts)

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Show your work:  (2 pts)
Part B: Probabilities and Odds
4. For this set of exercises, you will need one standard six sided dice. If you don’t have one, you can use virtual dice: https://www.random.org/dice/,  (40 points total)
a. First, let’s differentiate between “odds” and “probability”. 
  
How   are odds and probability different?
(2   pts)

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What   is the “odds of in favor” ratio?
(3   pts)

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What   is the “probability of an event” ratio?
  (3 pts)

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What   are the odds of rolling a three? (Simplify all fraction answers.)
  (2 pts)

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What   is the theoretical probability of rolling a three? (Simplify all fraction   answers.)
  (2 pts)

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b. Please reflect on the previous question’s answer outcome. First, convert the fraction to a percent. 
  

Percent Probability
 
Theoretical   Probability   (Rounded to the nearest whole percent.)
(2 pts)

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Next, given the “Likelihood Scale” table above, what term best describes your answer?
  

Likelihood Scale
 
Term
(2 pts)

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a. What if someone challenged you to NEVER roll a 3? If you were to roll the dice 18 times, what would be the empirical probability of never getting a three? 
  

Percent Probability
 
Solution:
(Rounded to the nearest whole percent.)
(2 pts)

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Show your work: (2 pts)
b. 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 pts)

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Likelihood Scale Term
(2 pts)

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

Percent Probability
 
Solution:
(Rounded to the nearest whole percent.)
(2 pts)

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Show your work:  (2 pts)
  
What   do you notice about the answers for parts c. and d. above?
(2 pts)

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d. Roll the dice 18 times and keep track of what is rolled in the table below. (2 points)
  
Roll   #

Dice

Roll   #

Dice

Roll   #

Dice
 
Roll 1

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Roll 7

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Roll 13

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Roll 2

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Roll 8

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Roll 14

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Roll 3

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Roll 9

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Roll 15

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Roll 4

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Roll 10

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Roll 16

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Roll 5

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Roll 11

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Roll 17

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Roll 6

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Roll 12

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Roll 18

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e. Based on your dice 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 pts)

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Likelihood Scale Term
(2 pts)

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Show your work:  (2 pts) 
  
In regards to the “Likelihood   Scale” terms for each, how did this differ from both the theoretical   and empirical probability?
(2 pts)

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