4. Hugo and Viviana work in an office with eight other coworkers. Out of these 10 workers,their boss needs to choose a group of four to work together on a project.(a) How many different working groups of four can the boss choose?(b) Suppose Hugo and Viviana absolutely refuse, under any circumstances, to worktogether. Under this restriction, how many different working groups of four canbe formed?

Step 1:Total 10 coworkers given.From this, the boss needs to select 4 workers for the project.Here,…

Answered: 4. Hugo and Viviana work in an office…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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?
(a) Of the 7 new programmers hired by a software company, 4 will work on web applications, 2 will work on desktop applications, and 1 will work on mobile applications. In how many ways can this arrangement be made? (b) Answer the same question if 8 programmers are hired (some of them will not be assigned to any task yet).
Problem:Fifteen books are to be placed in a shelf. The fifteen books are composed of the following: six structural engineering books, five geotechnical engineering books, and four water-resource engineering books. 1. In how many ways can you arrange the books if they must be grouped together? 2. In how many ways can you arrange the books if the geotechnical engineering books are grouped together?
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1. Read and analyze the following problems. Write your solution on a sheet of paper. The coach of the winning basketball team chooses 3 of the 15 members to be interviewed by a sports reporter. In how many ways can the members to be interviewed be chosen? A poker hand consists of 5 cards chosen at random from a standard deck of cards. How many poker hands containing all face cards are possible? 2. 3. Suppose 7 female and 6 male applicants have been successfully screened for 5 positions. In how many ways can the following compositions be selected? a. 5 people regardless of gender b. 3 females and 2 males C. at least 3 females d. 4 females and 1 male e. 5 females 4. In a game of poker, a full house is a combination of 5 cards chosen from a standard deck of cards with three of a kind and two of a kind. How many full houses are possible?
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