Applying Counting Techniques to a Real-World Scenario

I’m trying to study for my Mathematics course and I need some help to understand this question.

Hello,

I need some assistance solving this problem. There are two parts to this problem.

The Question is:

A random password generator is a computer program, hardware device, or online tool used to generate passwords using a set of parameters like length, letters, numbers, symbols, and strength (Nicholas, 2016).

Suppose that you want to create a password of four characters in length that can only include lower case letters and numbers from 0 to 9.

Part I: Answer the following questions:

1. Assuming repetitions are allowed, how many passwords are possible?
2. Assuming repetitions are not allowed, how many passwords are possible?
3. Assuming repetitions are not allowed and there must be exactly two numbers, how many passwords are possible?
4. Assuming repetitions are not allowed and there must be exactly two numbers, located at the end of the password, how many passwords are possible?
5. Assuming repetitions are not allowed, there must be exactly two numbers, located at the end of the password, and that the letters can only be vowels, how many passwords are possible?

Part II: Based on your work in Part I, discuss the following:

1. Explain your thought process to answer questions one through five in Part I. Identify which counting technique you used to answer each question.
2. Could you have used any other counting technique to answer question one, Part I? Justify your answer.
3. Could you have used any other counting technique to answer question two, Part I? Justify your answer.
4. Compare your answers to questions one and two in Part I. Elaborate on what happens when repetitions are allowed versus not allowed.
5. Compare your answers to questions three and four in Part I. Elaborate on what happens when you restrict the location of the two numbers.
6. Explain how you can use a tree diagram to answer question five, Part I. Do not actually include the tree diagram.
7. Compare your answers to questions one through five in Part I. Reflect about the security of passwords as more restrictions are added.
8. Think of another scenario where you can apply counting techniques. Discuss the advantages of knowing how to use counting techniques in the context of the scenario you created.

Reference

Nicholas, M. (2016). Dashlane blog [web log comment]. Retrieved from https://blog.dashlane.com/how-random-password-generators-work/ (Links to an external site.)

Requirements:

You must submit two files for this assignment. The first file should contain the computations, graphs, diagrams, etc., associated with the questions in Part I. This file may be formatted as a numbered list of answers. Unless stated in the problem, a narrative discussion is not required, but you must provide enough information to show how you arrived at the answer.

The second file should be a 2-3-page narrative paper, written in APA format, associated with the situation described in Part II.