Algebra

Lab and 10 question multiple choice quiz.

Must be able to remote connect to me via teamviewer or join.me to take the quiz.

MA1310: Week 10

Binomial Theorem, Counting Principle, Permutation, and Combination

This lab requires you to:

· Evaluate a binomial coefficient.

· Expand a binomial raised to a power.

· Find a particular term in a binomial expansion.

· Use the fundamental counting principle.

· Use the permutations formula.

· Distinguish between permutation problems and combination problems.

· Use the combinations formula.

The expression of Binomial Theorem occurs in computer science, statistics, finite mathematics, and calculus.

Permutations and combinations are used in our daily life all the time. The number of ways an event is performed can be counted based on these principles and methods. Some of the specific examples are the ways a committee can be formed or a football team can be formed. Ideally, we would live in a risk-free world. However, almost every action exposes people to some risk. Recognizing relative risks is important for a long and healthy life. Probability provides us with a measure of the likelihood that an event will occur. Knowledge about probability allows individuals to make informed decisions about their lives

Answer the following questions to complete this lab:

1. Define Binomial Coefficient. Give an example. Write the steps of a Graphing Utility to evaluate your Binomial Coefficient and the final answer.

2. Explain the fundamental counting principle in two to three sentences. Give an example.

3. State the difference between permutation and combination.

4. There are 14 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being the last stand-up comic of the evening, and one of the performers wants to be the first. If these performer’s requests are granted, how many different ways are there to schedule the appearances?

5. Of the 100 people in the U.S. Senate, 18 serve on the Foreign Relations Committee. How many ways are there to select Senate members for this committee (assuming party affiliation is not a factor in selection)?

6. A fair coin is tossed two times in succession. The set of equally likely outcomes is {HH, HT, TH, TT}. Find the probability of getting exactly two tails.

Submission Requirements: Answer all the questions included in the lab. You can submit your answers in a Microsoft Word document, or write your answers on paper and then scan and submit the paper. Name the file as InitialName_LastName_Lab10.1_Date.

Evaluation Criteria:

· Did you show the relevant steps in doing problems?

· Did you write thorough explanations for the short-answer questions?

· Did you submit your answers in an organized fashion that was legible and easy to follow?

· Were the answers correct?

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