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Combinatorics

Counting the number of integers

Counting ones. If you write down the integers between 1 year do you get a whole number when you divide the day number by the month number? For example, for December 24, the result of 24 divided by 12 is 2. Ways of solving and solution

Sample Means and Combinations

At the downtown office of First National Bank there are five tellers. Last week the tellers made the following number of errors each: 2, 3, 5, 3, and 5. a. How many different samples of 2 tellers are possible? b. List all possible samples of size 2 and compute the mean of each. c. Compute the mean of the sample means and

Permutations and Combinations - Counting Techniques

Create and example that reflects the formula that was given to us to use as an example in the counting techniques section. Example was: (See attachment) The answer to the question previously submitted was perfect Now I have to create an example the formula given.

Probability Experiment, Permutations, Combinations

Wk 5 1) Explain what outcomes of an experiment are. What does it mean to have equally likely outcomes? Provide examples to illustrate. 2) Explain permutations and combinations and the differences between the two. Use examples to illustrate.

Organized Counting and Permutations

1. On his university application, Enzo must list his course choices in order of preference. He must choose three of the four courses available in his major discipline, and two of the three courses offered in related subjects. In how many ways can Enzo list his course choices? Explain the reasoning for your answer. 2. How ma

Organized Counting and Combinations

Questions - u8 The questions are to be answered with full solutions. Be sure to focus on proper mathematical form, including: 1. One equal sign per line, 2. Equal signs in each question lined up vertically with each other, 3. No self-developed short form notations, 4. One step or idea per line, 5. Show complete solutio

Combinatorics: Example Problems

In furnishing their new office space, a company allows each employee to select a desk, a chair and a bookcase or file cabinet based on personal preference. There are two desk models, 3 different chairs, 2 styles of file cabinet and 4 bookcase styles to choose from. Given these possibilities, how many different office configurati

Permutations Combinations

Given the group {Allen, Brenda, Chad, Dorothy, Eric} you will be asked to determine a. the number of ways of choosing a president, vice-president and secretary/treasurer. (3 points) b. the number of ways of choosing a leadership team composed of 2 members. (3 points) c. the number of ways of choosing a president, vice-

Sets and counting

Combine algebraic sets to yield other sets, understand techniques for determining the number of elements in a set, and use permutations and combinations formulas to combine or arrange elements in a set. II. The three different media outlets of radio, Internet, and newspaper are to be offered on weekends or weekdays, and then

Statistics - Permutations and Combinations

1. THERE ARE 8 MEMBERS ON THE BOARD OF DIRECTORS. IF THEY MUST FORM A SUBCOMMITTEE OF 6 MEMBERS,HOW MANY DIFFERENT SUBCOMMITTEES ARE POSSIBLE? 2. HOW MANY WAYS CAN AN IRS AUDITOR SELECT 5 OF 12 TAX RETURNS FOR AN AUDIT? 3. THERE ARE 18 PEOPLE ON A BASEBALL TEAM. HOW MANY DIFFERENT ARRANGEMENTS OF CAPTAIN AND CO-CAPTAI

Equivalence Relations and Partitions

See attached Let R be the relation on the set {1,2} defined by 2R2 and the relation R holds for no other ordered pair except the pair (2,2). Show that R has exactly two of the three defining properties of an equivalence relation.

Procedural Steps for Combinations and Permutations

1) How many different ways can a teacher select 2 books from a possible 17 books? 2) How many different ways can be made from a test bank of 20 questions if the test consists of 5 questions? 3) How many different ways can 4 tickets be selected from 50 tickets if each tickets wins a different prize?

Probability and Combinations

The nation of Griddonesia consists of eighty-one equally-spaced islands represented by intersections of the lines in the following grid, where north is up and east is right as on a standard map. Each island is connected to all its adjacent islands by horizontal and vertical bridges exactly one-mile long. There are no diagonal br

Combinations: Unit gap in the interior of metal cube

A CE graduate student named Naresh is experimenting with large concrete block sizes. For a block size of 1 foot high by 1 foot wide by 3 feet long, he tries to pack as many blocks as possible into a 7 foot by 7 foot by 7 foot metal box. He soon realizes that it is impossible. There will always be a 1 foot by 1 foot by 1 foot gap

Counting Principles

I need help with these 6 problems Section 8.1 #14 Section 8.2 #20,46 Section 8.3 #26 Section 8.4 #8,16 14. A menu offers a choice of 3 salads, 8 main dishes, and 5 desserts. How many different meals consisting of one salad, one main dish, and one dessert are possible? 20. A group of 3 students is to be selected fro

25 Algebra Problems

How many different ways can you arrange FORMULA? .11984e7 1.024390e7 21 5040 5764801 An experiment of students randomly selected a letter from one of four boxes after first selecting a box at random. The first two boxes contain the letters s, o, h; the third contains c, a, h; and the fourth contains t, o , a. What is th

Permutation isomorphic

Please see the attached file. I need a detailed proof of this to study please. Permutation groups G1 and G2 acting on the sets S1 and S2 are called permutation isomorphic if there exists an isomorphism  : G1 ! G2 and a bijection  : S1 ! S2 such that (x)(s) = (xs) 8 x 2 G1 and s 2 S1. In other words, the following diagr

Complement, Union and Intersection of Sets

1. Describe (in words) two different sets of people containing you as a member. Describe (in words) the complement of each set. Describe what people are not in either the original set or the complement set. 2. Using the same two sets you described in problem 2, describe (in words) the new set formed by joining the two sets to

Combinatorics Proofs Combinatorics

See attached Show that for n, t, k>=1, the number of n-element multisets with elements of t types in which exactly k different types of elements occur...

Combine algebraic sets to yield other sets, understand techniques for determining the number of elements in a set, and use permutations and combinations formulas to combine or arrange elements in a set.

. II. The three different media outlets of radio, Internet, and newspaper are to be offered on weekends or weekdays, and then either between 7 a.m.-3 p.m., 3 p.m.-11 p.m. or 11 p.m.-7 a.m. How many different possibilities exist? List the possibilities and verify your listing with the multiplication principle for counting. I

Word Problems: How many different possibilities exist?

II. The three different media outlets of radio, Internet, and newspaper are to be offered on weekends or weekdays, and then either between 7 a.m.-3 p.m., 3 p.m.-11 p.m. or 11 p.m.-7 a.m. How many different possibilities exist? List the possibilities and verify your listing with the multiplication principle for counting.

Finding Probabilities: Counting Principles Example

At the first meeting of a committee to plan a Northern California pow-wow, there were 3 women and 3 men from the Miwok tribe, 2 men and 3 women from the Hoopa tribe and 4 women and 5 men from the Pomo tribe. If the ceremony subcouncil consists of 5 people, and it is randomly selected, find the probabilities that the subcouncil c

Cookie combinations

3.) A cookie company makes three kinds of cookies, oatmeal raisin, chocolate chip, and shortbread, packaged in small, medium, and large boxes. The small box contains 1 dozen oatmeal raisin and 1 dozen chocolate chip; the medium box has 2 dozen oatmeal raisin, 1 dozen chocolate chip, and 1 dozen shortbread; the large box contain

Counting technique

11.) There are two small towns, Greenville and Yellowville. Greenville contains 20 houses and Yellowville contains 15 houses. The state safety inspector is asked to randomly inspect 5 houses in Greenville and 7 houses in Yellowville. In how many ways can this be done (Hint: this is not a permutation)?

20 Combination Problems

Please show all work. Classify each problem according to whether it involves a permutation or a combination. 23. In how many ways can the letters of the word GLACIER be arranged? 24. A four-member committee is to be formed from a twelve-member board. In how many ways can it be formed? 27. In how many ways can nine differe

Mathematics - Algebra - Combinatorics

Suppose B is a proper subset of C. a. If n(C) 5 8, what is the maximum number of elements ... b. What is the least possible number of elements ... Suppose C is a subset of D and D is a ... Suppose you are playing a word game ... Use a Venn diagram to determine ... Case Eastern Junior College awarded 26 varsity

Simple Permutations or Combinations in Excel

Provide a simple Permutation or Combination problem and use Excel's PERMUT or COMBIN statistical commands to solve your problem. You can find PERMUT and COMBIN commands under Excel (Insert ---> Function ---> Statistical). Show the work.