Question 5Determine whether each of the following is an example of a permutation or combination;a) The number of ways a committee of 3 could be chosen from a group of 20.b) The number of ways a president, vice-president, and treasurer could be chosen from agroup of 20.c) List and explain 3 applications for probabilities of combination in daily life.

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Answered: Determine whether each of the following…

Advanced Engineering Mathematics

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Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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3. The Alumni of Saint Belousov University have decided to run a lottery in support of the University Tiddlywinks team. The lottery committee agree that ticket buyers will pick 5 letters from the 13 different letters that make up the name of the University: s, a, i, n, t, b, e, l, o, u, v, r, y. How many different tickets are possible if: (a) The order in which the letters are picked is not important and no letter may be repeated (eg. saint and stain give the same ticket.) (b) XXX The order is taken into account and letters may be repeated (eg. abbab and aabbb are different tickets) (c) XX The order is taken into account and letters may be repeated but exactly three of the letters must be vowels. (eg. asalo. Note: y is not considered to be a vowel in this instance.)
At a music festival, there are eight bands scheduled to play, numbered 1 through 8. a. How many different ways can these bands be arranged to perform? b. If band 7 is performing first and band 2 last, then how many ways can their appearances be scheduled?
An urn contains 5 red balls, 4 green balls, and 1 white ball. Three are drawn simultaneously. Answer the following questions: How many ways can 1 ball of each color be drawn? How many ways can at least 1 green ball be drawn? How many ways can the same color ball be drawn?
At a music festival, there are seven bands scheduled to play, numbered 1 through 7. a. How many different ways can these bands be arranged to perform? b. If band 2 is performing first and band 5 last, then how many ways can their appearances be scheduled?
Four members from a 43-person committee are to be selected randomly to serve as chairperson, vice-chairperson, secretary, and treasurer. The first person selected is the chairperson; the second, the vice-chairperson; the third, the secretary; and the fourth, the treasurer. How many different leadership structures are possible? There are possible different leadership structures. (Type an integer or fraction. Simplify your answer.)
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?
1. Assume that a class of 16 students is supposed to write an essay. If 3 essays are randomly selected to appear on the class bulletin board, how many different groups of 3are possible? (calculate number of combinations of 3 items from 16 available items).Show the result of calculations.
TOPIC: Problem Solving on Permutation and Combination. Analyze and Solve each problem. a) Out of 5 mathematicians and 7 engineers, a committee consisting of 2 mathematicians and 3 engineers is to be formed. In how many ways can this be done if one particular engineer must be in the committee? b) In a contest, there are 24 ways to choose the winners of the champion, the 1st runner-up, and the 2nd runner-up. How many contestants are there? c) In how many ways can the letters in "MATH IS FUN" be arranged if the first and the last letter must be vowels?
In how many ways can a class of 32 students select a president, vice president, treasurer, and secretary?
A computer programming team has twelve members. Suppose seven team members are women and five are men. How many groups of five can be chosen that contain two women and three men? (select the correct answer) O 165 ○ 210 ○ 350 O 125 ○ 56
How to solue X-2 by iteration? %3D X+2

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Determine whether each of the following is an example of a permutation or combination; ) The number of ways a committee of 3 could be chosen from a group of 20. ) The number of ways a president, vice-president, and treasurer could be chosen from a group of 20.