Applications Of Counting Techniques In This Unit You Have Se

Applications Of Counting Techniquesin This Unit You Have Seen The Dif

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.

Paper For Above instruction

In a corporate setting, a company is selecting a team of representatives to participate in an industry conference. The organization has a pool of 15 employees who have relevant experience and skills suited for the different roles within the conference team. The company needs to form a team of four members to attend and represent the organization. The key question is how many different groups of four employees can be chosen from the total pool of 15 employees? This scenario involves selecting a subset of individuals where the order does not matter, which makes it a classic case for the use of combinations.

The parameters for this problem are as follows: the total number of employees (n) is 15, and the number of employees to be selected (r) is 4. Since the order of choosing the team members is not important—what matters is who is on the team, not the sequence in which they are picked—the appropriate counting technique is the combination formula. The combination, denoted as C(n, r), is calculated as:

C(n, r) = n! / (r! (n - r)!)

Substituting the values, we have:

C(15, 4) = 15! / (4! (15 - 4)!) = 15! / (4! 11!)

Calculating the factorials, we get:

C(15, 4) = (15 × 14 × 13 × 12) / (4 × 3 × 2 × 1) = 32,760 / 24 = 1,365

Therefore, there are 1,365 different ways to select a four-person team from the pool of 15 employees to represent the company at the conference. This result illustrates how combinations help organizations evaluate all possible team choices where order does not matter, facilitating informed decision-making in team assembly situations.

References

• Arfken, G. (2013). Mathematical Methods for Physicists. Academic Press.
• Grinstead, C. M., & Snell, J. L. (1997). Introduction to Probability. American Mathematical Society.
• Ross, S. M. (2014). A First Course in Probability. Pearson.
• Blitzstein, J., & Hwang, J. (2014). Introduction to Probability. CRC Press.
• Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences. Cengage Learning.
• Winston, W. (2004). Operations Research: Applications and Algorithms. Duxbury Press.
• Johnson, R. A., & Kotz, S. (2005). Discrete Multivariate Distributions. Wiley-Interscience.
• Feller, W. (1968). An Introduction to Probability Theory and Its Applications. Wiley.
• McClave, J., Benson, P., & Sincich, T. (2014). Statistics for Business and Economics. Pearson.
• Grinstead, C. M., & Snell, J. L. (2000). Introduction to Probability. American Mathematical Society.