3. Ten national leaders are to be seated at around table at a summit. If the presidents ofthe US and Russia do not wish to be seatednext to each other, in how many ways canthis be done?

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Answered: 3. Ten national leaders are to be…

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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A large research project is looking for more researchers. There are 8 spots open on the research team. There are 10 mathematicians and 14 computer scientists that apply for the team. a. How many different ways can a team of 8 be made for the project? b. How many different ways can a team of 8 be made for the project if the team must contain at least one computer scientist and at least one mathematician.
Faculty at a certain university need to create a committee to evaluate the general studies curriculum offered on campus. If there are 25 faculty members and they must select a chair, vice chair, secretary and 4 additional faculty members to be on the committee, in how many ways can the committee be formed?
2. We have a group for 4 Americans, 3 Mexicans, 3 Germans, and 2 Canadians. a) In how many ways they can sit in a line next to each other? b) In how many ways, if all Americans must sit together? e) In how many ways, if all Americans must sit together and all Mexicans must sit together? d) In how many ways, if people from the same nation must sit together?
3. The students' council is having pizza at their next meeting. There are 20 council members, 6 of whom are vegetarian. A committee of 3 will order six pizzas from a pizza shop that has a special price for large pizzas with up to three toppings. The shop offers ten different toppings. a) How many different pizza committees can the council choose if there must be at least one vegetarian and one non-vegetarian on the committee?
8) A Company has 800 employees who bank with the Bank of Berba and First Public Bank. 312 bank with the Bank of Berba and 564 bank with the First Public Bank. How many employees bank with both banks, if 12 employees have no bank accounts?
1. Dr. Orchid has 9 paintings she wants to hang side by side on her wall. (a) In how many ways can she arrange all 9 paintings? Show your work. (b) If she only wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display? Show your work.
11. Consider 14 books: 6 Science, 5 Math, 3 English, to be arranged in a book shelf where only 7 books can be placed. How many ways a. Can one arrange with more than 4 Science books? b. Can one arrange with at least 2 Math books? Can one arrange without English books? C.
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3. A company checks its managers and find that 70 of them have an undergraduate degree in Business, 30 have an undergraduate degree in business and a Masters in Business, and 45 have only A Masters in Business. 20 others have neither degree. How many managers are in this company?
2. An emergency committee consisting of 12 health's officer staffs is chosen from 10 doctors and 12 nurses. Calculate the number of ways the committee is made up of: a. 5 doctors and 7 nurses. b. not more than 6 doctors. c. at least 3 doctors and 4 nurses.
We want to divide 12 children into any number of playgroups. However, in order to avoid some predictable disagreements, we want Adam and Brenda to be in different playgroups. How many ways are there to do this? (Playgroups have at least one child)
Let T : R2 → R² be the linear transformation which rotates vectors counter-clockwise about the origin by 7T/3 radians (60 degrees). (i) Find the standard matrix of the linear transformation T. (ii) Use your matrix to rotate the vector v = counterclockwise about the origin by 4 T/3 radians.

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3. Ten national leaders are to be seated at a round table at a summit. If the presidents of the US and Russia do not wish to be seated next to each other, in how many ways can this be done?