Test #2

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Combinatorics Topics For K-8 Teachers
MAT 305 Summer 1997

Roger Day
day@math.ilstu.edu

1.

Respond to each of these questions by placing your solution in the blank. You do not need to generate explanations for questions (a) through (e).

a.Express C(20,6) in terms of P(20,6).

b.How many distinct arrangements exist for the letters in the word TETRAMETER?

c.In the expansion of (w + x + y + z)^19, determine the value of the coefficient K in the collected term Kw^2x^9y^5z^3.

d.Express C(10,5) - C(9,5) as a single combination.

e.Express in simplest form the sum that includes every other term, starting with the first term, in the (ordered) 20th row of Pascal's Triangle.

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2.

How many ways can the letters in the word oblique be arranged so that no two consonants are adjacent?

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3.

Write the collected terms in the expansion of (w - 2k)^4. Simplify the numerical coefficients.

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4.

A flag is to be created for the new country of Slynskonskia. The country's founders agreed that:

  • the flag should be composed of three solid-colored horizontal stripes of identical width,
  • no two adjacent stripes could be the same color, and
  • there would be no designated "top" of "bottom" to the flag.

If there are five colors to choose from, how many different flags could be made for Slynskonskia under these conditions?

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5.

A city ballot includes 12 referendum questions. For each question, voters choose YES or NO to express their preference.

a.How many different marked ballots could be submitted, given that a choice of YES or NO is made for each of the 12 questions?

b.How many different marked ballots could show 5 questions marked YES and 7 questions marked NO, given that a choice of YES or NO is made for each of the 12 questions?

c.If voters may abstain from choosing a response on any and all questions, how many different ballots could be submitted by voters?

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6.

A game of super-dominoes is played with pieces divided into three cells instead of the usual two. The set contains all possible triplets of values from triple blank to triple six, with no duplications. For example, the set does not include both 2-3-1 and 1-3-2 because these are simply reversals of each other. The set does contain 3-1-2, however.

How many pieces are in the set?

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