2. There are 12 students in a party. Five of them are girls. In how many ways canthese 12 students be arranged in a row ifa) there are no restrictions?b) the 5 girls must be together (forming a block)?c) no 2 girls are adjacent?d) between two particular boys A and B, there are no boys but exactly 3girls?

Answered: Image /qna-images/answer/64d934c1-a59b-4282-9775-1436d4e03cec.jpg

Answered: 2. There are 12 students in a party.…

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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Q2) A club has 20 member a) In how many different ways could the club choose a president and a vice president? b) In how many different ways could the club choose two co-presidents? c) In how many different ways could the club choose a president, vice- president, and secretary? d) In how many different ways could the club choose a three-member governing committee? e) In how many different ways could the club choose two co-presidents and a secretary?
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?
4. How many ways are there to seat 7 people at a round table in the following two different situations? a) Everyone can sit anywhere. b) Certain two people should not be sitting next to each other
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?
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)
Q6) An eight-man committee is to be formed from a group of 10 welsh-men and 15 Englishmen. In how many ways can the committee be chosen if i) ii) iii) The committee must cotain 4 of each nationality. There must be more Welshmen than Englishmen. There must be at least two welshmem.
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A volleyball team consists of 14 players: There are 6 rookies and the rest of the players are veterans. a) In how many ways can they select a group of 4 to play a sand volleyball game if exactly three of the players must be rookies. b) In how many ways can they select a group of 4 to play a sand volleyball game if at least three of the players must be rookies.
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.
Among the eight nominees for two vacancies on a school board are four men and four women. How many ways can the vacancies be filled a) With any two of the eight nominees? b)With any two of the female nominees? c) With any one of the male nominees and one of the female nominees?
Please keep in mind that the order of the students sitting matters so you should use permutation

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