3. Eight different people want to interview for the Defense Against the Dark Arts professorship at Hogwarts:Severus Snape, Tom Riddle, Remus Lupin, Dolores Umbridge, Mad-Eye Moody, Quirinus Quirrell, Barty Crouch, andGilderoy Lockhart.Albus Dumbledore needs to interview the candidates.How many possible orders are there in which Dumbledore can interview the candidates if all of the following conditionsmust be simultaneously true?Snape must be interviewed before Riddle,• Dolores Umbridge is interviewed last,• Crouch and Moody must be interviewed at the same time in a joint interview, ANDLupin and Lockhart are interviewed consecutively (although we do not know which of the two is interviewed first)

Given data is: The conditions are:

Answered: 3. Eight different people want to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose that there are five young women and six young men on an island. Each woman is willing to marry some of the men on the island and each man is willing to marry any woman who is willing to marry him. Suppose that Anna is willing to marry Jason, Larry, and Matt; Barbara is willing to marry Kevin and Larry; Carol is willing to marry Jason, Nick, and Oscar; Diane is willing to marry Jason, Larry, Nick, and Oscar; and Elizabeth is willing to marry Jason and Matt. Identify the correct statements with respect to the matching between men and women formed in the previous question. (Check all that apply.) Check All That Apply It is a complete matching from the set of women to the set of men. It is not a complete matching from the set of women to the set of men. It is a maximum matching, since complete matching is always a maximum matching. × × It is not a maximum matching, because complete matching need not be always a maximum matching. ×
Consider the following problem: Three officers-a president, a treasurer, and a secretary-are to be chosen from among four people: Ann, Bob, Cyd, and Dan. Suppose that, for various reasons, Ann cannot be president and either Cyd or Dan must be secretary. How many ways can the officers be chosen?
3. Maria and John have decided that once they live in a house, they want to have a pet. They go to an animal shelter and find several pets that they would love to take home. There are 3 Siamese cats, 3 German Shepherds, 9 Labrador Retrievers, and 22 mixed breed dogs. Since they can’t decide, they place all the adoption cards in a container and draw one. Answer each of the following questions separately, showing all your work to reach each answer. A. What is the probability that they select a cat? B. What is the probability that they select either a German Shepherd or a Labrador Retriever? C. What is the probability that if they select a dog, that it is not a mixed breed? D. What are the odds in favor of and against choosing a Siamese cat?
Three different classes contain 20, 18, and 25 students, respectively, and no student is a member of more than one class. If a team is to be composed of one student from each of these three classes, in how many different ways can the members of the team be chosen?
A company is organizing a team-building event with various activities. There are 12 employees attending the event, and they need to be split into three teams: Team A, Team B, and Team C. Each team should have at least 2 members but no more than 6 members. In how many different ways can the teams be formed? (Note: The order of the teams doesn't matter; i.e., Team A, Team B, and Team C is the same as Team C, Team A, and Team B.)
A, B, C, D and E go on a holiday by car. (a) In how many different ways can they choose the seats in the car, if there are any five seats? Order matters. (b) Suppose a car has three back seats. In how many different ways do they can the people sitting in the back seats choose? The order doesn't matter. (c) A has promised to act as a car driver. In how many different ways can the rest of the people choose the seats in the car, if the car has seven seats (in addition to the driver's seat)?
Two new drugs are to be tested using a group of 60 laboratory mice, each tagged with a number for identification purposes. Drug A is to be given to 21 mice, drug B is to be given to another 21 mice, and the remaining 18 mice are to be used as controls. How many ways can the assignment of treatments to mice be made? (A single assignment involves specifying the treatment for each mouse—whether drug A, drug B, or no drug.) (Enter the exact number or an equivalent algebraic expression.)
3. Mr. Jones intends to place 10 books on his bookshelves. Among these, 4 are books on mathematics, 3 are books on chemistry, 2 are books on history, and 1 is a book on a foreign language. Jones wants to arrange his books so that all the books dealing with the same subject are together on the shelf. How many different arrangements are possible?
4. Hugo and Viviana work in an office with eight other coworkers. Out of these 10 workers, their boss needs to choose a group of four to work together on a project. (a) How many different working groups of four can the boss choose? (b) Suppose Hugo and Viviana absolutely refuse, under any circumstances, to work together. Under this restriction, how many different working groups of four can be formed?
In a survey of 500 students in a university, 200 are enrolled in Psych 101, 180 are enrolled in Spanish 200, 170 are enrolled in French 10, 40 in Psych 101 and Spanish 200, 45 in Spanish 200 and French 10, 50 in Psych 101 and French 10, and 15 in all the three courses. How many students are enrolled in:a. Any of the three courses b. Not in Psych 101 or not in French 10 c. not in both Psych 101 and French 10
Suppose we want to choose 4 objects, without replacement, from 17 distinct objects. (a) If the order of the choices is not relevant, how many ways can this be done? (b) If the order of the choices is relevant, how many ways can this be done?
Suppose we want to choose 5 objects, without replacement, from 9 distinct objects. (a) If the order of the choices is not taken into consideration, how many ways can this be done? (b) If the order of the choices is taken into consideration, how many ways can this be done?

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