3. If we have 80 (identical) tennis balls and 20 identical bags to place them in, how many waysare there to distribute the tennis balls into the bags if(a) the bags are required to be non-empty;(b) we allow bags to be empty3;(c) all bags are required to be non-empty, 10 of the bags can only contain an odd number oftennis balls and the remaining 10 bags can only contain an even number of tennis balls.(Hint: for (c) introduce a parameter (t say) to count the number of balls put in the oddbags.)

Given: We have 80 tennis balls and 20 bags that are identical. Under the following circumstances, we…

Answered: 3. If we have 80 (identical) tennis…

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 the captain of a ship that is in distress must send a total of eleven different signals in succession. The eleven signals com- prise of 4 blue light signals (B1, B2, B3 and B4), 4 purple light signals (P1, P2, P3 and P4) and 3 red light signals (R1, R2 and R3). He must send the signals one after another at 1 minute intervals. In how many different ways may the captain send the signals if the purple light signals are the first 4 signals and the red light signals are the last 3 signals? [Answer]
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?
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 twenty-something single person is planning a ski vacation. Assume that he has 2 possible destinations: Utah, and Oregon. There are 4 ski areas in Utah with 4 available times for 3 of the areas, and 1 times for the other area. There are 4 ski areas in Oregon with 2 available times for 3 of the areas, and 4 times for the other area. (A "time" refers to a weekend for which there are vacancies at the ski lodge.) A trip plan involves the selection of a location, ski area, and a time. How many possible plans are there?
4) Mendoza's Pizzeria offers many wonderful topping options on their world-famous pizza pies. A cheese pizza costs $20, plus it costs $1 for any veggie topping (onions, green peppers, spinach, etc), and $2 for any meat topping (pepperoni, bacon, sausage, etc.). There must be at least 2 toppings on each pizza pie, but there cannot be more than 10 toppings on any one pie. Marty enters the scene with $30 in his pocket. a. Write a system of inequalities that represents the constraints on the number of each topping that can be included on Marty's pizza.

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