8 Congressmen are to be divided at random into three committees on ed- ucation, the economy and foreign policy, respectively. Each committee will consist of exactly six Congressmen (assume that order does not matter within the committees, but that it does matter on which committee a Congressman will serve). (a) In how many different ways can this be done? (b) Suppose that of the 18 Congressmen, 6 are Republicans, 9 are Democrats, and 3 are Independents. What is the probability that in a random committee assignment all the Independents end up on the same committee?

8 Congressmen are to be divided at random into three committees on ed- ucation, the economy and foreign policy, respectively. Each committee will consist of exactly six Congressmen (assume that order does not matter within the committees, but that it does matter on which committee a Congressman will serve). (a) In how many different ways can this be done? (b) Suppose that of the 18 Congressmen, 6 are Republicans, 9 are Democrats, and 3 are Independents. What is the probability that in a random committee assignment all the Independents end up on the same committee?

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...

See similar textbooks

Similar questions

Suppose there are 5 men and 8 women qualified to be members of a new committee of 6 people, includinga president, a vice-president, and a secretary.(a) How many different ways do you have to pick a president, vice-president and secretary if you need atleast 1 men and 1 women? Does the order matter? Why?(b) How many different committees can you form with at least 3 women? Does the order matter? Why?
Suppose there are 14 freshman, 13 sophomores, 15 juniors, and 17 seniors running for the offices of president, vice president, and secretary. If no person can hold more than one office, in how many different ways could these people be elected to these positions?
A student planning her curriculum for the upcoming year must select one of three business courses, one of five mathematics courses, two of ten elective courses, and either one of four history courses or one of three social science courses. How many different curricula are available for her consideration? different curricula
Assume that the committee consists of 14 members including Julie. The same three offices are to be filled. (1) In how many different ways can the offices be filled if each person can hold at most one office? (2) In how many of these ways is Julie the chairperson? (3) In how many of these ways is Julie an officer?
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 survey of 1,046 tourists visiting Orlando was taken. Of those surveyed: 254 tourists had visited the Magic Kingdom 263 tourists had visited LEGOLAND 57 tourists had visited both the Magic Kingdom and LEGOLAND 55 tourists had visited both the Magic Kingdom and Universal Studios 55 tourists had visited both LEGOLAND and Universal Studios 31 tourists had visited all three theme parks 82 tourists did not visit any of these theme parks How many tourists only visited the Universal Studios (of these three)?
Company C has 20 employees who are available to serve on a new committee. If the committee will consist of six members at large, the number of different possible committees is __________.
The Student Engineering Council at a certain college has one representative from each of the five engineering majors (civil, electrical, industrial, biological, and mechanical). In how many ways can (a) a president, a vice president, and a secretary be selected? (b) both a council president and a vie president be selected?
Quen: In a pharmaceutical study, two drugs (A and B) and a placebo are to be compared for effects. Fifty people are to be used in the study, of whom 20 are to receive drug A, 20 receive drug B, and the remainder receive the placebo. Assuming the people are numbered 1 to 50, how many different ways could the assignment of the drugs and placebo be made?