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Solve the Equations, Permutations and Combinations

1. As a business owner, there are many decisions that you need to make on a daily basis, such as ensuring you reach the highest production levels possible with your company's products. Your company produces two models of bicycles: Model A and Model B. * Model A takes 2 hours to assemble. * Model B takes 3 hours to assemble.

Set Definitions with Unions and Intersections

Exercises on Sets 1. Please provide a short definition of the following: a. Set b. Subset c. Proper Subset d. Complement of a set e. Union of a set f. Intersection of a set Solve following problems showing your work: 2. Set X = {3, 7, 11, 21, 39, 43, 567}, Set Y = {1, 3, 6, 8, 11, 42, 567} a. What is

Running Time of a Set Union Implementation

The input consists of two arrays each representing a set of integers (in each array, each value appears only once). The output is an array representing the union of the two sets - again, each value appears only once. Write a method to implement set union and analyze its running time.

Combinatorial problems with counting principles

1. Use the theorem below to determine the number of nonequivalent colorings of the corners of a rectangle that is not a square with the colors red and blue. Do the same with p colors. (the answer is (p^4+3p^2)/4...i just dont know how to get there) Theorem: Let G be a group of permutations of X and let C be a set of color

Probability distributions, probability, combinations, permutations

Mat 102 1. How many different 5-digit sequences can be formed using the digits 0,1,....8 if repetition of digits is allowed? Use the multiplication principle to solve the problem 2. A shirt company has 4 designs each of which can be made with short or long sleeves. There are 7 color patterns available. How many different

Generating Permutations and Combinations

The Complement A of an r-subset A of {1,2...,n} is the (n-r)-subset of {1,2,...,n} consisting of all those elements that do not belong to A. Let M= C(n,r), the number of r subsets and at the same time the number of (n-r)-subsets of {1,2...,n}. Prove that if A1,A2,A3...AM are the r subsets in lexigraphic order then complements Am

total number of possibilities

1. in how many ways can five identical rooks be placed on the squares of an 8 by 8 board so that four of them forma the corners of a rectangle with sides parallel to the sides of the board. 2. consider and 9 by 9 board and nine rooks of which five are red and four are blue. suppose you place the rooks on the board in nonattac


1. Four (standard) dice (cubes with 1,2,3,4,5,6 respectively,dots on their six faces) each of a different color are tossed each landing with one of its faces up, thereby showing a number of dots. Determine the following probabilities. a. the probability that the total number of dots shown is 6 b. the probability that at most


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

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

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

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-

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

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

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

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

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

Relations and sets

1) Find a relation R on a set S that is neither Symmetric nor antisymmetric 2) Let S be a set containing exactly n elements. How many antisymmetric relations on S are there. 3) give a recursive definition of X^n for any positive integer n 4) give a recursive definition of the nth odd positive integer 5) Let g: Z -> Z

Counting and subsets

Use the formula for the number of subsets of a set with n elements to solve the problem. 1. Pasta comes with tomato sauce and can be ordered with some , all, or none of these ingredients in the sauce: {onions, garlic, carrots, broccoli,shrimp, mushrooms, zucchini, green pepper}. How many different variations are available for

Standard Combinatorics

Problem 1) We have 20 kinds of presents; and we have a large supply of each kind. We want to give presents to 12 children. It is not required that every child gets something; but no child can get 2 copies of the same present. In how many ways can we give presents? Problem 2) List all subsets of {a,b,c,d,e} containi

Set Partitions and Bit Strings

Which of these collections of subsets are partitions on the set of bit strings of length 8? a) The set of bit strings that end with 00; the set of bit strings that end with 01; the set of bit strings that end with 10; and the set of bit strings that end with 11. b) The set of bit strings that end with 111; the set of bit


A representative of the Environmental Protection Agency wants to select samples from 10 landfills. The director has 15 landfills from which she can collect samples. How many different samples are possible?