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# Combinatorics

### Combinations

1 a. consider the multiset {n times a, 1,2,3,...n} of size 2n. Determine the number of its n- combinations. b. consider the multiset {n times a, n times b, 1,2,3...,n+1} of size 3n+1. Determine the number of its n- combinations.

### Probability that a randomly selected United States resident

3,. Explain what outcomes of an experiment are. What does it mean to have equally likely outcomes? Provide examples to illustrate. Solution: Outcomes of an experiment are the results of any performed experiment. Two equally likely outcomes indicate that each of these outcomes appeared the same number of times. Like whil

### Statistics - Permutations, Combinations or neither

Decide if the situation involves permutations, combination's or neither. The number of ways 17 people can line up in a row for concert tickets. Does the situation involve permutations, combination's or neither? (choose correct answer a, b or c) a) Permutations. The order of 17 people in line matters. b) Neit

### 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.

### Four Students are running for presidency in their dormitory

Four Students are running for presidency in their dormitory: Debra, Farah Jorge and Hillary. Who is declared the new president using the Borda count method? See attached file for the whole problem.

### 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.

### Permutation Rank of Gray Code

I need a detailed solution of the attached problem. Recall the "Gray code"-like listing of all the permutations....

### 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