Department

MathematicsCourse Code

MAT 409Professor

AllStudy Guide

MidtermThis

**preview**shows pages 1-2. to view the full**8 pages of the document.**MAT 409

Test #3 Name

_________________

60 points

Impact on Course Grade: approximately 10% Score _________________

Solve each problem based on the information provided. It is not necessary to complete every

calculation. That is, your responses may contain combinatorial notation (factorials, exponents,

combinations, permutations). Include explanations as needed.

You are to work alone on this test. You may not use anyone else's work. You may refer to one or more

sheets showing general difference tables, and you must turn in such information with your test

responses. You may not refer to any other materials as you complete the test. You may ask me

questions. You may use a calculator, but no other technology tools. You may not make internet

connections, search the web, or use any sort of mental telepathy.

Evaluation Criteria

Each of questions 1 through 6 is worth 10 points. Some questions have more than one part. For each

question and each part, a point assignment is indicated.

Some questions require explanation and some do not. Read carefully and ask me if you need help in

determining whether an explanation is required.

For questions requiring explanation:

• Approximately 60% of the points revolve around a correct solution to the problem. I will

evaluate the mathematics you use:

o Is it accurate and appropriate?

o Have you provided adequate justification?

• Approximately 40% of the points count toward how you express your solution. I will evaluate

how you communicate your results:

o Is your solution clear and complete?

o Have you expressed logical connections among components of your solution?

The BONUS! is worth 7 points, including 4 points for (I) and 3 pts for (II).

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

1. Write the correct answer on the blank provided. No explanation or justification is required. (10 pts total)

(a) Determine the value M that satisfies the equation !",$

%= 𝐶(9,7). (2 pts)

_______________

(b) Consider the word BIVOUACKED. (2 pts each)

(i) Determine the number of unique arrangements for the letters in this word. ____________

(ii) Suppose the consonants in this word must be kept non-adjacent. How many

unique arrangements of the letters are there under this condition?

_______________

(c) Consider the word STRENGTHLESSNESS. (2 pts each)

(i) Determine the number of unique arrangements for the letters in this word.

_______________

(ii) How many unique arrangements of the letters are there if the arrangement must begin and

end with the letter T and all letters S must be kept together?

_______________

###### You're Reading a Preview

Unlock to view full version

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

2. For this problem, consider a standard deck of 52 playing cards.

(a) How many unique hands of 5 cards exist? (2 pts)

_______________

(b) How many ways can 5 cards be dealt to a card player? (2 pts) ______________________

(c) A 5-card hand that contains 3-of-a-kind of one card value and 2-of-a-kind of a different card

value is called a full house. For example, a hand with 4♥, 4♠, 4♦, and 7♥, 7♣ (“three 4’s and

two 7’s,” called fours over sevens) is a full house. How many different full-house 5-card hands

are possible? (3 pts)

_______________

(d) How many ways are there for two players to have a total of k cards? It is permissible that the

two players may not each have the same number of cards. (3 pts)

_______________

###### You're Reading a Preview

Unlock to view full version