oriamot lo59. Out of 5 mathematicians and 7 statisticians, a committee consisting of 2mathematicians and 3 statisticians is to be formed. In how many ways can this be done if(a) any mathematician and any statistician can be included, (b) one particular statisticianmust be on the committee, (c) two particular mathematicians cannot be on the committee?

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Answered: 59. Out of 5 mathematicians and 7…

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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There are 8 men and 7 women employed in an office from whom a selection committee of 4 has to be formed in order to select a new employee. (a) How many committees can be formed? (b) How many committees can be formed with at least 2 men? (c) Suppose one member in the committee has to be appointed as Head of the committee. Then, how many committees are possible?
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4. In how many different ways can we select a committee consisting of 4 engineers 3 chemists, and 2 mathematicians from 7 engineers, 5 chemists, and 7 mathematicians?
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A 4-person grievance committee is to be selected out of 2 departments, A and B, with 10 and 30 people, respectively. In how many ways can the following committees be selected? Complete parts (A) through (E) below. (A) 3 from A and 1 from B (B) 2 from A and 2 from B (C) All from A (D) 4 people regardless of department (F) At least 2 from department
A committee of 5 is chosen from 10 men and 6 women. Determine the number of ways of selectingthe committee if:(i) there are no restrictions (ii) it must contain 3 men and 2 women (iii) it must contain at least 3 men (iv) it must contain at least one of each sex.
A hospital working group of 8, consisting of 3 doctors, 2 nurses and 3 lawyers is to be put together. 6 doctors are available to serve on the working group, 4 nurses and 4 lawyers are available. How many different possibilities are there for the membership of the working group?
A club has 13 women and 7 men. They decided that at leats two women should represent them on the committee of 8. Under this restriction, how many different groups from this club are possible?
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?

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