Explore BrainMass

# Combinatorics

### 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

### Counting Letter Combinations

Please explain thoroughly. Show or draw diagram. 1. How many four-letter words can be formed from the set of letters{m,o,n,e,y} ? Assume that any arrangement of letters is a word.How many four -letter words can be formed if the first letter must be y and the last letter must be m?( Assume no repetition).

### Example of a Permutation or Combination

Program Selection. A meeting is to be addressed by 5 speakers, A, B, C, D, and E. In how many ways can the speakers be ordered if B must come first? Please show which formula is used.

### 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.

### Counting rule for permutations and combinations

P n,r = n!/(n - r)!, Cn,r = n!/r!(n-r)! a) Compute P 8,3 b) Compute C 8,3

### Compare the value of three Corporate or Grand Strategies in your organization.

Compare and contrast the value of three separate, grand strategies for your organization. What questions must each grand strategy answer? Who in the organization does the strategy affect and how? Prescribe a grand strategy for the organization. Explain the reasons for your recommendation.

### USE the Formula - Permutation Equation

NPr to evaluate the following expression 5P5

### Counting Techniques for a Limited Menu

A restaurant offers the following limited menu. MAIN COURSE: turkey, spaghetti, meatloaf, shrimp. hamburger VEGETABLES: broccoli, carrots, potatoes BEVERAGES : coffee, tea, milk, soda DESSERTS: sundaes, mousse, pie, brownies IF ONE ITEM IS FROM EACH OF THE FOUR GROUPS, IN HOW MANY WAYS CAN A MEAL BE ORDERED?

### Permutation and Combination - Evaluate: a) P6,4 b) C7,2 c) P4,4 d) C9,0

Evaluate: a) P6,4 b) C7,2 c) P4,4 d) C9,0

### Sets - List the elements in the set.1

Write the word or phrase that best completes each statement or answers the question. List the elements in the set. 1. Let U = { q,r,s,t,u,v,w,x,y,z} A = { q,s,u,w,y} B = {q,s,y,z,} C = { v,w,x,y,z} a. (A INTERSECT B') U (B INTERSECT A') B. A'-C Use the formula for the number of subsets o

### Fundamental Counting Principle - Automobile Models

An automobile manufacturer produces 7 models, each available in 6 different exterior colors, with 4 different upholstery fabrics and 5 interior colors. How many varieties of automobiles are available?

### 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

### Mathematics - Problems with Sets

Please show all steps. Thank you. Express the set using set- builder notation. Use inequality notation to express the condition x must meet in order to be a member of the set. 1. A= { 12, 13, 14, 15, 16,...} 2. A= { 600, 601, 602,...,6000} 3. Calculate the number of subsets and the number of proper subsets for

### Set Builders

Please explain. Thank you. Are the Sets equivalent? Justify Your answers. 1. A= { 14, 15, 16, 17, 18,} B= {13, 14, 15, 16, 17} 2. A= { 17, 18, 18, 19, 19,19,20, 20, 20, 20} B= { 20, 19, 18, 17} 3. A= { Larry, Moe, Curly, Shemp} B= { Posh, Sporty, Baby, Scary} Are the sets equal? Justify your ans

### 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

### Set Notation

Let A= {n element of Z : n=4q+1 for q element of Z} B= {m element of Z : m=8r-3 for r element of Z} Prove: a) A is in B b) B is in A C) A=B in set notation.

### Permutations and combinations..

In the design of an electrical product, 7 different components are to be stacked in a cylindrical casing that holds 12 components,in a manner that minimizes the impact of shocks. One end of the casing is designated as the top and the other end the bottom. a) how many different designs are possible b) If the seven compon

### Probability-If three sensors are selected at random for inspection, what is the probability that the system will be found in a failed state?

An over temperature warning system has five temperature sensors. To prevent false alarms, the system is designed so that three or more of the sensors must sense over temperature before a warning signal is given. Assume that the probability of any single sensor failing is equal likely and that three sensors are in a failed state.

### Let A, B and C be sets.

College level proof before real analysis. Please see the attached file.

### Proof for Images of Sets

College level proof before Real Analysis. Please kindly explain each step of your solution. 11. Let f: A --> B, and let {D_alpha: alpha is an element of Delta} an {E_Beta: Beta is an element of pi} be families of subsets of A and B, respectively. Prove that (see attached).

### Image of Sets

3. Let f(x) = 1 - 2x. Find (a) f(A) where A = {-1, 0, 1, 2, 3} (b) b(N) (c) f^-1(R) (d) f^-1([2, 5]). (e) f((1, 4]) (f) f(f^-1(f[3,4])))

### Define (a) random experiment, (b) sample space, (c) simple event, and (d) compound event.

1. Define (a) random experiment, (b) sample space, (c) simple event, and (d) compound event. 2. What are the three approaches to determining probability? Explain the differences among them. 3. Sketch a Venn diagram to illustrate (a) complement of an event, (b) union of two events, (c) intersection of two events, (d) mutually e

### Write each of the following permutations as a product of disjoint cycles.

Please see the attached file for the fully formatted problems.

### Counting Bitstrings

How many bitstrings of length 10 are there that contain 5(or more) consecutive 0's or contain 5(or more) consecutive 1's? Justify your answer.

### Give an example of nonempty sets A

College level proof before real analysis. Please give formal proof. Please explain each step of your solution. Thank you.

### A secondary math lesson plan is transformed into one appropriate for elementary school. Many ideas for math teachers of all ages are included.

I have a lesson plan but it is for 10th grade and wanted to know if you might be able to help me turn it into a 5th grade math plan?

### You are required to develop a useful classroom lesson plan based on research and appropriate educational philosophy.

You are required to develop a useful classroom lesson plan based on research and appropriate educational philosophy. You may not use a lesson plan from an already published source. Plan to use at least two different instructional strategies. Within the lesson plan, the following components must to be addressed: 1. Goals and

### 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

### Combinatorics Color Objects

Problem1) What is the number of ways to color n objects with 3 colors if every color must be used at least once? problem2) prove that for any three sets A,B,C ; ((AB) U (BA))^ C = ((A^C) U (B^C)) (A^B^C) ^ means intersection Please explain the steps, help me under