Option #1: Counting Principles #1

Write a report that answers the following questions and meet the list of requirements that follows.

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.


  1. How many ways can three dogs and four cats be selected from a group of three dogs and eight cats?
  2. To log into your laptop, a four-character code must be entered. The code must use the digits 0 through 9 or the symbols @, #, %, or &. If digits and symbols cannot be repeated, how many four-character codes can be created?
  3. A restaurant allows you to order a salad that includes five ingredients. Your choice of ingredients includes eight types of vegetables, two types of cheese, and three types of meat. How many unique, five-ingredient salads can be created?


  • Your paper should be 2-3 pages in length and should cite and integrate at least one credible outside source.
  • Include a title page, an introduction, a body, a conclusion, and a Reference list.
  • The introduction should summarize the problem and state what approach and method will be applied to solve it.
  • The body of your paper should answer the questions posed in the problem, explain how you approached and approached and answered the question or solved the problem, and for each question, show all steps involved.
  • The conclusion should summarize your findings and what you have determined from the data and your analysis, with a broader or personal perspective in mind when applicable.
  • As with all written assignments, provide in-text citations and a reference page.
  • Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.
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