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)
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)
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.
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.
3.Your community has asked you to help the Young Men's Christian Association (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 10 for each age group? (15 points total for Question 3)
For this set of exercises, you will need one standard six-sided dice. If you do not have one, you can use virtual dice: https://www.random.org/dice/ (40 points total for Question 4)
a.First, differentiate between odds and probability.
b.Reflect on the previous question’s answer outcome. First, convert the fraction to a percent.
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?
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.
e.Roll the dice 18 times and keep track of what is rolled in the table below. (2 points)
f.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.