Problem: Fifteen books are to be placed in a shelf. The fifteen books are composed of the following: six structural engineering books, five geotechnical engineering books, and four water-resource engineering books. 1. In how many ways can you arrange the books if they must be grouped together? 2. In how many ways can you arrange the books if the geotechnical engineering books are grouped together?

Problem: Fifteen books are to be placed in a shelf. The fifteen books are composed of the following: six structural engineering books, five geotechnical engineering books, and four water-resource engineering books. 1. In how many ways can you arrange the books if they must be grouped together? 2. In how many ways can you arrange the books if the geotechnical engineering books are grouped together?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2.) The BOS-14 is the new model of cars manufactured by NUC Motors. This model can be achieved in 2 body styles, 4 interior options and 7 different colors. The model can be achieved in automatic transmission as a manual. ER Auto wants to have a model of each of the options available to sell. How many BOS-14 models should you order?
7. A family consisting of 3 children and 10 adults have reserved a row of seats at a theater. The 3 children need to sit in the middle with 5 adults on either side. How many ways can the family seat themselves?
6. Felicia is working on the following problem: There are 730 balls to be put into packages of 3. How many packages can be made, and how many balls will be left over? Here are Felicia's ideas: 12 a. Explain may help 1200 ÷ 4 One hundred packages of balls will use 300 balls. After another 100 packages, we will have used up 600 balls. Another 30 packages will use another 90 balls, for a total of 690 balls used. b. Write equ and that remainde 9. Describe ho Ten more packages brings us to 720 balls used. Three more packages will bring us to 729 balls used. Then there is 1 ball left over. All together we and the deci explain why 10. Show how t could make 100 + 100 + 30 + 10 + 3 = 243 packages of balls with 1 ball left over. decimal repr
4. An open box is to be made from a square piece of cardboard, 18 inches by 18 inches, by cutting out equal squares from each corner and folding up the flaps to form the sides. Find the dimensions of the largest box that can be constructed in this way?
Part 4: Suppose that 53 of the 55 Computer Science students of San Sebastian College, Manila are taking at least one of the mathematics subjects Algebra, Trigonometry and Calculus. See the figure below for more details: 24 taking Algebra, 26 taking Trigonometry, 20 taking Calculus, 5 taking Algebra and Trigonometry, 7 taking Algebra and Calculus, 8 taking Trigonometry and Calculus. a. Find the number of students who are taking all three mäthematics subjects. b. Fill in the correct number of students in each of the eight regions of the Venn diagram. c. Determine the number of students who are not taking any of the three mathematics subjects? d. How many students are taking Algebra as their only mathematics subject? e. How many students were taking Calculus and Trigonometry but not Algebra?
11. Elyse is making punch for a party that requires 2 parts of fruit juice for every 5 parts of ginger ale. To make the punch, she uses 18 ounces of fruit juice and 3 containers of ginger ale. How many ounces are in each container of ginger ale?
38) SET UP ONLY: A business has 3 machines that manufacture containers. Together they can make 100 containers per day, whereas the two fastest machines can make 80 containers per day. The fastest machine makes 34 more containers per day than the slowest machine. How many containers can each machine make per day?
PART IV. Solve the following problems. You have eight books and are going to put four on a bookshelf. How many different ways can the books be ordered on the bookshelf? 1. You have seven books and are going to randomly select three to read. How many different combinations of books might you select?
7. At a tuition centre, some teachers teach English while others teach mathematics or both subjects. Fifty-two teachers teach English and 38 teachers teach mathematics. Of these, 22 teachers teach both subjects. How many teachers are there in the tuition centre?
1. You're making snowmen with your friends over break. For every 0 pointi snowman, you need 2 rocks for eyes, 3 rocks for buttons, and 1 carrot for a nose. How many rocks and carrots do you need if you want to make 5 snowmen?
3. It takes me 5 hours to weed all of the gardens at my house. If my husband works with me, it will take us two less hours to weed all of the gardens (than it takes me working alone). If Mr. King did this job on his own, how long would it take him? Show all of your work to receive full credit