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 empty;(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.)

We have 80 identical tennis ball and 20 identical bags . We need to calculate number of ways to fill…

Answered: ) the bags are required 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 survey of farmers showed that of the farmers, 124 grew only wheat, 108 grew only corn, 89 grew only oats, 201 grew wheat, 59 grew wheat and corn, 51 grew wheat and oats, and 181 grew corn. Determine the number of farmers who a) grew at least one of the three, b) grew all three, c) did not grow any of the three, and d) grew exactly two of the three.. calculator
5. a.) Threatened and in the U.S.? b.) An endangered foreign bitd? s c.) A mammal or a threatened foreign species? d.) If the species is threatened and foreign, it is a mammal? e.) The species is an amphibian? f.) The species is a reptile, endangered and not foreign? g.) The species is not endangered? h.) Assume the species is endangered, what's the probability that it is a bird and that it's from the U.S.?
c) There are three train tracks from village X to village Y and four train tracks from village Y to village Z. i) How many ways to travel from village X to village Z via village Y by train? ii) How many different round-trip routes are there from village X to Y to Z to Y and back to X in which the same road cannot be travelled twice?
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In a class of 280 first year students, 65 study only Spanish, 100 study Chemistry, 175 study Mathematics, 18 study Spanish and Chemistry, 75 study Chemistry and Math, 20 study Math and Spanish and 15 study all three subject. a) How many students study exactly one of these subjects?b) How many students study Chemistry and Math, but not Spanish?c) How many students study none of these subjects?d) How many students study Spanish or Chemistry?
a class consists of 37 freshmen, 54 sophomores, and 22 juniors. The class wantsto send a nine-person delegation to the university sentate a) if the delegation has to consist of 2 freshman 3 sophomore, and 4 juniors, how many different delegation are possible? b) If the nine-person delegation is chosen without regard to class standing, how many delegations are possible?
Computer programming team has 13 members. B.) Suppose 7 are women and 6 are men. How many groups of 5 can be chosen to only one being a man? B2) Suppose 2 insist on working together or not at all on projects. How many groups of 5 can be chosen to work on a project?
1. A class of 16 students contains five Math majors, seven Engineering majors and four Physics majors. A group of three students from the class is to be selected to form a team for an academic competition. a.) How many teams can be formed that have a representative from each major? b.) How many teams can be formed that have exactly one Math major? c.) How many teams can be formed that have at least one Math major?
e) d) In how many ways can the letters of the word "OPTOM" be arranged? Show work. A committee of 3 is to be formed from a group of 20 people. How many different committees are possible? Show work. f) From a group of 5 women and 7 men, how many different committees consisting of 2 women and 3 men can be formed? Show work.
In drawing 3 CD’s from a lot, defective and non defective CD’s , let A, B , C and D mean at least one Defective CD, at least one non defective CD, 2 defective CD’s and 2 non defective CD’s, respectively. Are A and B mutually exclusive? Are C and D mutually exclusive? Comment on your results.

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) the bags are required to be non-empty; ) we allow bags to be empty; ) all bags are required to be non-empty, 10 of the bags can only c