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For this Critical Thinking assignment, you will apply counting techniques to real-world scenarios.

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:**

- Assuming repetitions are allowed, how many passwords are possible?
- Assuming repetitions are not allowed, how many passwords are possible?
- Assuming repetitions are not allowed and there must be exactly two numbers, how many passwords are possible?
- Assuming repetitions are not allowed and there must be exactly two numbers, located at the end of the password, how many passwords are possible?
- 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:**

- Explain your thought process to answer questions one through five in Part I. Identify which counting technique you used to answer each question.
- Could you have used any other counting technique to answer question one, Part I? Justify your answer.
- Could you have used any other counting technique to answer question two, Part I? Justify your answer.
- Compare your answers to questions one and two in Part I. Elaborate on what happens when repetitions are allowed versus not allowed.
- Compare your answers to questions three and four in Part I. Elaborate on what happens when you restrict the location of the two numbers.
- Explain how you can use a tree diagram to answer question five, Part I. Do not actually include the tree diagram.
- Compare your answers to questions one through five in Part I. Reflect about the security of passwords as more restrictions are added.
- 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.

**References**

Nicholas, M. (2016). __How do random password generators work?Ā (Links to an external site.)__ *Dashlane.*__Ā (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. Specific requirements for the paper are provided below:

- Your paper should be 2-3 pages in length (not counting the title page and references page) and should cite and integrate at least two credible outside sources. The CSU Global Library is a great place to find resources. Your textbook is a credible resource.
- Include a title page, introduction, body, conclusion, and a reference page.
- The introduction should describe or summarize the topic or problem. It might discuss the general applications of the topic or it might introduce the unique terminology associated with the topic.
- The body of your paper should address the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.
- The conclusion should summarize your thoughts about what you have determined from your analysis in completing the assignment. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.

- Include any tables of data or calculations, calculated values, and/or graphs referenced in the paper. (Note: The minimum required length excludes any tables, graphs, etc.)
- Document formatting, citations, and style should conform to the
__CSU Global Writing CenterĀ (Links to an external site.)__. A short summary containing much that you need to know about paper formatting, citations, and references is contained in theĀ__Template PaperĀ (Links to an external site.)__. If you need assistance with your writing style or you need writing tips or tutorials, visit theĀ__CSU Global Writing Center.__