1. You are ordering 15 sandwiches for delivery from a deli that sells Chicken salad,Turkey, Peanut butter, Roast beef, and Hummus sandwiches.a) How many ways can you order 15 sandwiches and get exactly 4 Chicken saladsandwiches?b) How many ways can you order 15 sandwiches and get exactly 4 Chicken saladsandwiches or exactly 4 Peanut butter sandwiches?c) How many ways can you order 15 sandwiches and get exactly 4 Chicken salador exactly 4 Peanut butter or exactly 4 Hummus sandwiches?d) How does your reasoning and your answers to the previous three questionschange if we change every "exactly" to an "at least"?2. Let S = {m, a, t, h, f, u, n}, |S| = 7.a) How many 4-element subsets of S contain m or a?b) How many 4-element subsets of S contain m, a or t?c) How many 4-element subsets of S contain m, a or do not contain t?d) How many subsets of S contain m or a?e) How many subsets of S contain m or a or t?f) How many subsets of S contain m or a or do not contain t?3. A marble set is a collection of 20 red marbles, 25 blue marbles, 22 green marblesand 28 yellow marbles.a) How many ways can you select a subset of 7 marbles with exactly 2 red orexactly 2 blue marbles?b) How many ways can you select a subset of 7 marbles with exactly 2 red marblesor exactly 2 blue marbles or exactly 2 yellow marbles?c) How many ways can you select a subset of 7 marbles and get at least 6 yellowmarbles?

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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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5.
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.
12. A donut shop has 8 different types of donuts available. a) How many different ways are there to pick out a dozen donuts? b) How many different ways are there to pick out a dozen donuts if you want no more than 4 of any one type?
2. In how many ways can the 7 Harry Potter books be arranged on a shelf?
a) Dave is choosing classes. He can choose from 4 different math classes, 3 different writing classes, and 7 different humanities classes. He needs to pick one of each of math, writing, and humanities. How many different schedules can Dave make? b) Dave goes to the squirrel farm to buy 6 squirrels. There are 19 different squirrels to pick from. How many ways can Dave choose the 6 he buys?
1. How many arrangements could be made of the word GRATEFUL if: o there are no restrictions? o the first letter is a vowel and the last letter is a consonant? o the first three letters are vowels? 1. Jessie starts from home and walks three (3) blocks north and five (5) blocks east to the library. From the library, she travels four (4) blocks north and seven (7) blocks east to the pizzeria. o How many different routes can Jessie take to go from home to the library if she is always moving closer to the library? o How many different routes can Jessie take to go from home to the pizzeria if she is always moving closer to the pizzeria? 1. A teacher must select five (5) students to attend a conference. She has 11 males and 13 females to choose from. Determine the number of way of selecting: o a group of five with no restrictions o exactly 3 females o at least 4 males o at most 3 females
a).A food-processing firm has 8 brands of seasoning agents from which it wishes to prepare a gift package containing 5 seasoning agents. How many combinations of seasoning agents are available? b). A sales person has 9 products to display in a trade fair but he can display only 4 at a time, how many displays can he make if the order in which he displays is important? c).A radio repairer notes that the time he spends on his job has an exponential distribution with a mean of 4 minutes. He follows the first come first serve principle. The arrival time of clients takes a Poisson distribution with an average rate of 8 clients every 1 hour. i.Determine the arrival rate value and service rate value to be used ii) How long will it take the client waiting in the queue iii). Determine the client’s average waiting time in the system iv).Compute the probability that the system is idle; P (idle)
42. A certain restaurant prepared meals during the pandemic for the first-responders. If they prepared 4 spaghetti meals for every 7 meat meals, how many meat meals were there if there were 385 meals prepared?
A Hawaiian favorite food is the "loco moco." It consists of a bed of rice under a meat patty with an egg on top smothered in brown gravy. The rice can be white or brown, the egg can be fried, scrambled, or poached, and the meat can be hamburger, Spam, Portuguese sausage, bacon, turkey, hot dog, salmon, or mahi. How many different loco mocos can be ordered?

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