question archive Applications of Counting Techniques In this unit, you have seen the differences between combinations and permutations as well as how to calculate the results for each type of counting application

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**Applications of Counting Techniques**

In this unit, you have seen the differences between combinations and permutations as well as how to calculate the results for each type of counting application. For example, say you would like to form a focus group on improving your software with individuals who took an initial survey. How many different three-person focus groups can be formed from the 20 people who originally took the survey? (Combination problem)

If you want your three-person focus group to have one person serve as the spokesperson for the group, one person as the notetaker, and one person as the timekeeper, how many different focus groups can you form with these three positions, drawing from the total group of 20 people? (Permutation problem)

**Post 1: Initial Response**

Compose a counting question that applies either the combination or permutation formula (i.e., focus the development of your question to draw upon one of these two counting techniques, specifically). Please include the following information:

- Provide a description of the situation, including how many people or items you may select from in total (n) and how many will make up the outcome (r).
- Clearly state the counting question which can be addressed based on this situation.
- Identify the counting technique required to answer the question and show the steps for determining the solution.
- Express the solution in a complete, narrative sentence, tying in some of the original context from the situation you described above to clearly communicate your result.