3. A delegation of 4 students is selected each year from a technical school to attend the Skills Olympicsof Students.(i) In how many ways can the delegation is chosen if there are 12 qualified students?(ii) In how many ways if two of the qualified students will not attend the Olympics together?(iii) In how many ways if two of the qualified students are brothers and will only attend the Olympicstogether?

Answered: Image /qna-images/answer/4379fc7b-35eb-4789-9e4d-4cf9e0840244.jpg

Answered: 3. A delegation of 4 students is…

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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Similar questions

8. How many ways are there for four men and seven women to stand in a line so that (a) All men stand together and all women stand together? (b) All men stand together? (c) All women stand together? (d) All men stand together or all women stand together?
1. Dr. Orchid has 9 paintings she wants to hang side by side on her wall. (a) In how many ways can she arrange all 9 paintings? Show your work. (b) If she only wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display? Show your work.
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?
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?
Suppose we want to choose 5 objects, without replacement, from 15 distinct objects. How many ways can this be done, if the order of the choices is not relevant? (b) How many ways can this be done, if the order of the choices is relevant?
4. A company’s CEO has 8 people reporting directly to her, and she wantsto select 2 to attend the grand opening of a new retail store. How many possible ways are there of selecting 2 people to attend?
Twelve officers of an organization are to be divided into committees. In how many ways can the officers be divided into three committees composed of six, four, and two members, respectively? O 12 C6 +12 C4 +12 C2 O 12 C6 *12 C4 *12 C2 O (12)(4)(2) 12 6 4 2,
A debate team of 4 members is to be formed from a group of 25 students. How many possible teams are possible given the following conditions? a)One of the team members has to be the first speaker, another one has to be the second speaker, a third one has to be the first reply speaker and the other one has to be the second reply speaker. (b) Two of the team members have to be speakers and the two other members of the team have to be reply speakers. (c) No particular role is assigned to any of the students.
4. In a bakery, there are 12 kinds of cookies and there are 25 cookies available from each kind. a) In how many ways can we buy at least 1 cookie from this bakery? b) In how many ways can we buy at most 2 cookies from this bakery? c) In how many ways can we buy exactly 4 cookies from this bakery?
6. A jar is to be filled with 100 jelly beans. There are five varieties of beans to choose fromn and we are required to use between 10 and 50 beans of each variety. How many different ways of filling the jar are there?
32. A track coach must choose a 4-person 400 m relay team and a 4-person 800 m relay team from a squad of 7 sprinters, and of whom can run on either team. If the fastest runner sprints last in both races, in how many ways can the coach form the two teams if each of the 6 remaining sprinters runs only once and each different order is counted as a different team?

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