7. A school committee of six members will be selected from a group of two administrators, fiveteachers, and eight students.a) How many ways can a group be formed if it must include exactly four students. [1b) What is the probability that Mr. Healy, a teacher, is on the committee but no administrators arechosen for this committee?..

Solution:-a) To calculate the number of ways a group can be formed with exactly four students, we…

Answered: 7. A school committee of six members…

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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8. In a class of 16 students, 4 are undergrads. For the final project, students are randomly divided into 4 groups. a. What is probability that each group has only 1 undergrad, if the groups are of equal size? b. What is the probability that each group has I undergrad, if groups have at least1 student?
9. In a group of 30 people, 10 have blue eyes. If a committee of 5 people is randomly selected, what is the probability that exactly 2 of them have blue eyes?
A school has 200 students with 80 students taking each of the three subjects trig, probability, and basket-weaving. There are 30 students taking any given pair of these subjects, and 15 students taking all three subjects. A) How many students are taking non of these three subjects? B) How many students are taking only probability?
4. A gumball machine contains 60 gumballs of which 15 are yellow, 25 are pink, and 20 are blue. To operate the machine, you put a nickel into the slot and a random gumball is dispensed. If you buy 10 gumballs, what is the probability that: a) You get 2 yellow gumballs? b) All the gumballs are the same color?
30. The chess clubs of two schools consists of, respectively, 8 and 9 players. four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that exactly one of Rebecca and Elise will be chosen to represent her school? Show the STEP-BY-STEP SOLUTION CLEARLY. SHOW EXPLAMATIONS IF NECESSARY.
6.) A mathematics class has 16 engineers majors, 12 science majors, and 4 liberal artsmajors.a.) What is the probability that a student selected at random will be a science orliberal arts major?b.) What is the probability that a student selected at random will be anengineering or science major?c.) 5 of the engineering students, 6 or the science majors, and 2 of the liberal artsmajors are female. What is the probability that a student selected at random is anengineering major or a female?
A student-faculty government committee of 4 people is to be formed from 20 student volunteers and 5 faculty volunteers. a. If one person from the group of volunteers is chosen at random to draw the names out of a hat, what is the probability that the person drawing the names is a student? b.How many ways can the committee of four be formed if there are no restrictions on composition. c. How many ways can two of the students be chosen? d. How many ways can 2 faculty be chosen? e. What is the probability that the random selection of the four-person committee will result in two students and two faculty?
1. In a candy jar, there are 20 blueberry and 12 cherry gumballs. If you randomly select two gumballs from this jar, what is the probability that both of them are the same flavor?Round your answer to 3 places after the decimal point, if necessary; or enter your answer as a fraction. 2. In the manufacturing division of a particular company, there are 79 managers and 38 supervisors. If two employees from the manufacturing division are randomly selected to represent the company at an upcoming conference, what is the probability that both employees have the same job title?Round your answer to 3 places after the decimal point, if necessary; or enter your answer as a fraction. 3.
A. Suppose you close your eyes and randomly select one M&M from your pile, find the probability of grabbing a color that contains the letter “r”or a color that contains the letter “o”. B. Suppose you close your eyes and randomly select one M&M from your pile, replace that M&M, and select another M&M from the pile. What is the probability that you will select an orange and a yellow M&M? C. Suppose you close your eyes and randomly select two M&M’s from your pile, without replacing the first M&M. What is the probability that you will select a red and a blue M&M?
8. The composition of the 108th Congress is 50 Republicans, 48 Democrats, and 2 Independent. A committee on aid to higher education is to be formed with 3 Senators to be chosen at random to head the committee. Find the probability that the group of 3 consists of a. All Democrats b. One Democrat, one Republican, and one Independent
A committee is to consist of a chair, three hagglers, and five do-nothings. The committee is formed by choosing randomly from a pool of 11 people and assigning them to the various "jobs." 1. How many different committees are possible? 2. Norman is eager to be the chair of the committee. What is the probability that he will get his wish? 3. Norman's girlfriend Norma is less ambitious and would be happy to hold any position on the committee provided that Norman is also selected as a committee member. What is the probability that she will get her wish and serve on the committee? 4. Norma does not get along with Oona (who is also in the pool of prospective members) and would be most unhappy if Oona were to chair the committee. Find the probability that all Norma's wishes will be fulfilled: She and Norman are on the committee, and it is not chaired by Oona.

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