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Midterm

# MAT 409 Illinois State 409Test03S18Exam

Department
Mathematics
Course Code
MAT 409
Professor
All
Study Guide
Midterm

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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
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).

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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?
_______________

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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)
_______________