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

A survey of 1,059 tourists visiting Orlando was taken. Of those surveyed: 291 tourists had visited the Magic Kingdom 290 tourists had visited LEGOLAND 298 tourists had visited Universal Studios 99 tourists had visited both the Magic Kingdom and LEGOLAND 66 tourists had visited both the Magic Kingdom and Universal Studios 51 tourists had visited both LEGOLAND and Universal Studios 12 tourists had visited all three theme parks How many tourists had not visited any of these three theme parks?
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)?
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?
5 members from the math department, 5 members from the biology department, 5 members from the English department, 5 members from the history department, and 5 members from the physics department have declared themselves candidates for three vacant faculty senate seats. If the three seats must be filled by three members from three different departments, in how many ways can the vacant seats be filled?
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?