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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?

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

Interpretation and Comparison of Combination Permutation

1. This week we were introduced to new terminology and symbols. Please interpret the symbol P(B|A) and explain what is meant by the expression. Why is P(B|A) not the same as P(B)? 2. Consider the formulas: nPr =n!/(n-r)! and nCr = n!/(n-r)!r! a. Given the same values for n and r in each formula, which is the smaller val

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?

Combinations in Committees and Groups

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,

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

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

Permutations and Restrictions

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)

Finance : Combinations, Interest, Annuities and Loans

1) An admissions test given by a university contains 10 true-false questions. Eight or more of the questions must be answered correctly in order to be admitted. a) How many different ways can the answer sheet be filled out? b) How many different ways can the answer sheet be filled out so that 8 or more questions are answere

Combinations and Permutations : Six Problems

1) Give clearly justified answers to the following. a) How many 7-digit telephone numbers can be formed if the first digit cannot be 0 or 9 and if the last digit is greater than or equal to 2 and less than or equal to 3? Repeated digits are allowed. b) How many different ways are there to arrange the 6 letters of the word CA

Order of a Permutation

Please see the attached file for the fully formatted problems. Find the order of sigma^1000, where sigma is the permutation (123456789) (378945216) Find the order of , where is the permutation . Solution. Since and . Let ,

Combinations, Permutations and Truth Tables

1. (a) How many license plates can a state produce if the plates can contain 6 characters (from 26 letters and 10 digits) if they can only use one digit? (b) How many ways can Mr. Paul choose 6 students from a class of 15 Boys and 12 Girls, if he must choose at least 5 boys? (c) How many orderings are there of the letter

Combinations : Seating Arrangements at a Dinner Table

In how many ways can 6 couples be seated at a circular table if each couple is not to be separated? How many ways can 5 Manchester United and 8 Chlesea players be seated at a circular dinner table if no two Manchester United players can sit together?

Permutations and combinations

A set of 10 flags, 5 red, 3 blue and 2 yellow are to be arranged in a line along a balcony. If flags of the same colour are INDISTINGUISHABLE, find the number of arrangements in which, 1) The three blue flags are together 2) The yellow flags are not together 3) The red flags occupy alternate positions in the line 4) If the