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Mathematics & Economics
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Counting (Other (Not Listed) Sample)


Module 5: Critical Thinking
View Grade InfoGrade: N/A
Critical Thinking Assignment (60 Points)
Important! Read First
Choose one of the following two assignments to complete this week. Do not complete both assignments. Identify your assignment choice in the title of your submission.
Option #1: Counting Principles #1
Write a paper that adheres to the Written Assignment Requirements in the CSU-Global Guide to Writing and APA Requirements. In addition, the items noted in the Good Writing Tips section should be observed.
Your paper should contain a title page, an introduction, a body, a conclusion, and possibly a list of references. The introduction should provide background information about your paper topic, and it should state what your paper will address. It often states the main idea or purpose of the paper in what is termed a thesis statement.
The body of your paper details your methodology, findings, and/or the results of analysis. APA requires that tables, figures, and calculations/formulas used in your paper appear in the paper body.
The conclusion is where we summarize our findings, state other conclusions, relay personal experiences, and sometimes discuss the “take-home” messages associated with our work. As with many written assignments, in-text citations and a reference page are often included.
Be sure to describe or define the Fundamental Counting Principle, combinations, and permutations in your paper introduction. Include detailed calculations and solutions in the body of your paper. 
In your paper, answer the following three questions:
Question #1 
How many nine-digit student identification numbers can be created from letters and numbers if the first four characters must be upper case letters from A to D and the last five must be digits from 0 to 9? Repetition of letters and numbers is not allowed.
Question #2 
Five Card Draw is a poker game in which each player is dealt an initial hand of five cards from a 52-card deck. How many unique five-card hands are possible?
Question #3
To log into your smart phone, a four-digit code must be entered. The code must use the digits 0 through 9 or upper case letters A through D. If digits and number can be repeated, how many four-digit codes can be created?


Date of Submission:
Ordering different objects or numbers could be challenging in the absence of appropriate knowledge. However, individuals with knowledge in areas such as the fundamental counting principle, permutations, and combinations can help solve such problems easily. The fundamental counting principle states that two independent events with m and n outcomes have the product  QUOTE  as the number of outcomes if the events occur together(Smith, 2012). Similarly, permutation is a mathematical technique used for ordering a collection of things systematically. Ultimately, combination is a mathematical technique used for selecting items from a larger group (Harshbarger, 2013). This paper uses numerical examples to demonstrate how to use the combinations and the fundamental counting principle.
Question One
The fundamental counting principle and permutations are applicable when solving this problem because selection of letters is independent from the selection of numbers (Smith, 2012). The procedure below demonstrates how to solve the problem.
There are four possible letters ABCD and ten digits from 0 to 9, which can se...
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