I need initial post and 2 responses to classmates. See attached for classmates posts.
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.
View Unit 3 Discussion Post 1 example.
Post 2: Reply to a Classmate
Select a question from a classmate’s initial response. Address all of the following.
Rewrite the question so that it draws upon the alternate counting technique (e.g., if they posted initially about combinations, you will rewrite the question to relate to permutations, or vice versa). Try to keep the same number of how many people or items you may select from in total (n) and how many will make up the outcome (r).
Show the steps for determining the solution to the new question you have written.
Express the solution in a complete, narrative sentence, tying in some of the original context from the situation your classmate began and which you revised slightly with your new question, to clearly communicate your result.
View Unit 3 Discussion Post 2 example.
Post 3: Reply to Another Classmate
Select a discussion thread in which both types of counting techniques have been applied. In complete, narrative sentences, summarize the results of applying the combinations versus permutations counting techniques in similar contexts by reviewing the different posts in this discussion thread. Use the following questions to develop your post:
What was the total count of possible outcomes when applying combinations? When applying permutations?
How did the results differ between these two techniques?
Why does it make any difference whether you are concerned about the arrangement, or order, of the objects or not?
How much of an influence does this factor (i.e., order matters versus order does not matter) appear to have on the results?Post 1
There are 128 runners from 27 countries competing in a track meet. The betting pool needs to know how many outcomes there may be for the top 3 finishers. How many different outcomes are there for the top 3 with 128 runners?
To answer this permutation all that is needed is to multiply the number of runners by the (number of runners minus one) until the number of places is equivalent to the number of multiplications used.
128 * 127 * 126 = 2048256 or P(128, 3)
There are 2048256 possible outcomes for the top 3 finishers of the track meet.
During a selection for a special duty, the judges had to pick 5 people from 15 contestants. How many different groups could you get from the 15 contestants? This would be a combination type of question. The order does not matter.
N = 15 (Total number of contestants)
R = 5 (Total number that will be picked)
15!/(15-5)!5! = 8!/10!5! = 3003
Now you can see there is 3003 ways to pick for the 5 person team of the 15 who applied.
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