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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Discrete Math : In a group of 65 students there are 30 math majors and 35 computing science majors. In how many ways can a committee of 6 students be selected if: (a) there are no restrictions (b) there must be 5 math majors and 1 computing science major (c) there must be more computing science majors than math majors (d) there is a chair that must be a math major, a vice-chair that must be a computing science major and then 4 other committee members. (Type your answers below. You do not have to calculate the actual number. e.g. 34 * C(8,3) would be fine.)
In a group of 200 students, the following facts are known: 75 are taking French, 80 are taking Japanese, 65 are taking English, 22 are taking both French and Japanese, 30 are taking French and English, 25 are taking Japanese and English, and 10 are taking all three-language courses. Find the following: a) The number of students taking exactly one course. b) The number of students not taking any course. c) The number of students who are taking both Japanese and French but not English. d) The number of students who are taking only French. e) The number of students taking any course.
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?
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.)
A bagel shop has bagels in the following six varieties: plain, sesame, onion, blueberry, asiagocheese, and everything. Assuming there are at least 20 bagels of each variety, how many waysare there to choose 20 bagels...a. with no restrictions.b. with three or fewer blueberry bagels.c. with three or fewer blueberry bagels and three or fewer onion bagels.
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
The Tiny State College Student Advisory Board has rules to the effect that the officers of the board (i.e., Chairperson, Vice-Chairperson, and Treasurer) must always include at least one in-state student and at least one senior. The TSC Student Council consists of 6 members: 1 in-state senior, two in-state students who are not seniors, 1 out-of-state senior, and two out-of-state students who are not seniors. In how many ways can the officers of the Student Advisory Board be selected from these 6 Student Council members if they must obey the rules? Note that if individual members switch offices, this produces a different Board.
6. A lead role and a supporting role are to be chosen from a drama club consisting of 40 talents. How many various choices of actors are possible if: there are no restrictions? ( (1) (ii) actor Kristoff will participate only if he is the lead role? ( (ii) actors Jess and Jet will act together or not at all? (iv) actors Keanne and Gian will not act together?

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