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Combinatorics

Random walk

Hi I would appreciate if you could help me with this question. Is the question below TRUE or FALSE and explain why ? Question: I have two random walks, both starting at 0 and with a reflecting boundary at 0. Each Step, Walk A goes up 1 with probability 1/2 and down 1 with probability 1/2(except at the boundary). Each

Sets, Counting and Grouping

Out of 30 job applicants, 11 are female, 17 are college graduates, 7 are bilingual, 3 are female college graduates, 2 are bilingual woman, 6 are bilingual college graduates, and 2 are bilingual female college graduates. What is the number of women who are not college graduates but nevertheless are bilingual?

How different statistical devices can be used in business?

How the following statistical devices can be used in business today? Describe their usefulness and how businessman can be benefit, or how to help them in making sound decisions. (Explain individually) --probability --probability distributions --normal distribution --permutation and combinations

Combinations : Application Word Problems (5 Problems)

2. A group pf 12 students have been hired by the city this summer to work as ground keepers. (a) During their first week of employment, half will be assigned to pick up garbage down town while the other half go on a training course. The second week, they will switch places. In how many distinct ways can 12 students be assigned

Finding Different Combinations

Imagine you've been left in charge of an ice cream stall and you have three flavours of ice cream to sell - vanilla, strawberry and chocolate. If you're selling triples (a cone with three scoops) how many different combinations can you sell?

Well Ordered Set : Proof of Refelxive and Transitive under Relation

Trying to prove the following: A set "A" is called a well ordered set if there is a relation R on A such that R is reflexive, transitive, and for all a,b are elements of A, either aRb or bRa. Prove that the set of the integers is a well-ordered set under the relation less than or equal to. Would I just need to prove th

Permutation Groups : Inverse and Product

Let alpha = [1 2 3 4 5 6] beta = [1 2 3 4 5 6] [2 1 3 4 6 5] [6 1 2 4 3 5] Compute each of the following: a) alpha^-1 b) alpha beta Please see attached for full question.

Probability : Permutations and Probability Distributions

1. You dream of someday winning the lottery (don't we all). You found out about a new lottery where the winning numbers are five different numbers between 1 and 34 inclusive. To win the lottery, you must select the correct 5 numbers in the same order in which they were drawn. According to your calculations, the probability of wi

Sets and counting

Six people are going to travel to Mexico City by car. There are six seats available in the car. In how many different ways can the six people be seated in the car if only three of them can drive?

Set Operations : Union, Intersection, Complement and Number of Elements

Use the information provided to determine the correct answers U={1,5,10,15,20,25,30} A={1,10,15} B={1,10,20,25} C={5,15,30} a.) A U B b.) C ^ B' (the ^ is supposed to be an upside down U) c.) (A ^ C') U B d.) n(A U B)' E.) use the sets provided to draw a venn diagram illistrating the relationsh

In how many ways can a man divide 7 gifts among his 3 children if the eldest is to receive 3 gifts and the others 2 each? From a group of n people, suppose that we want to choose a committee of k, k <=n, one of whom is to be designated as a chairperson. By focusing first on the choice of the committee and then on the choice of the chair, argue that there are (n choose k)?k possible choices.

5. In how many ways can a man divide 7 gifts among his 3 children if the eldest is to receive 3 gifts and the others 2 each? 6. From a group of n people, suppose that we want to choose a committee of k, k <= n, one of whom is to be designated as a chairperson. (a) By focusing first on the choice of the committee and then

Permutation Groups : Cycles

Here's my problem: Let (i1, i2, . . . , ik) be a k-cycle (k less or equal to n) element of Sn and let sigma be an element of Sn. (i) Find a precise expression for sigma * (i1, i2, . . . , ik)* sigma-inverse. Hint: experiment a little, perhaps, then take a guess and prove it. (ii) Describe precisely the set {sigma * (1,

Fields, Elements and Cyclic Groups

Find H K in {see attachment}, if H = <|3|> and K = <|5|>. This is all the problem says. I know the answer, but I do not know the reasoning.

Permutation groups

Show that in any group of permutations, the set of all even permutations forms a subgroup.

Important Information about Counting

Eight people are attending a seminar in a room with eight chairs. In the middle of the seminar, there is a break and everyone leaves the room. a) In how many ways can the group sit down after the break so that no-one is in the same chair as before? b) In how many ways can the group sit down after the break so that exactly

Introductory probability, basic combination/permutation

There is a lottery in which 2000 individuals enter, and of these a set of 120 names will be randomly selected. Assume that both you and your friend are entered in the lottery. a. In how many ways can 120 names be randomly selected from the 2000 in the drawing? b. In how many ways can the drawing be done in such a way that

Partitions on a Set

We denote the number of partitions of a set of n elements by P(n). Suppose the number of partitions of a set on n elements into k parts is denoted by P(n,k). Then obviously P(n) = P(n,1) + P(n,2) + ..... + P(n,n) Show that P(n,2) = 2^(n-1) - 1

Counting

A. An office manager has four employees and nine reports to be done. In how many ways can the reports be assigned to the employees so that each employee has at least one report to do. b. Find the number of ways to put eight different books in five boxes, if no box is allowed to be empty.

Probability

An automobile license number contains 1 or 2 letters followed by a 4 digit number. Compute the maximum number of different licenses.

Characterizing the metric space {N}

For the metric space { N }, the set of all natural numbers, characterize whether or not it has the following properties: compact, totally bounded, has the Heine-Borel property, complete. For compact, we are to show that every sequence converges. For totally bounded, we are to show that it can be covered by finitely many sets

Using Permutations and Combinations

Can you check my answers and help me with B? Preparing a plate of cookies for 8 children, 3 types cookies {chocolate chip, peanut butter, oatmeal}, unlimited amount of cookies in supply but only cookie per child. One cookie per plate, one plate per child. A) How many different plates can be prepared? C(8,3) = 56 B)