- #Discrete mathematics ensley crawley 2.3 solutions manual
- #Discrete mathematics ensley crawley 2.3 solutions license
(b) Roberta and Candice can finish among the top three runners in 6 ways. So the trophies can be awarded in P(30,8) = 301/22! ways. (a) Here we are dealing with the permutations of 30 objects (the runners) taken 8 (the first eight finishing positions) at a time.
#Discrete mathematics ensley crawley 2.3 solutions license
Based on the evidence supplied by Jennifer and Tiffany, from the rule of product we find that there are2x2xlxl0xl0x2 = 800 different license plates.
Consequently, 5040 - 840 = 4200 slates include at least one physician. (iii) There axe 7圆x5x4 = 840 slates where no physician is nominated for any of the four offices. (a) From the rule of product there are 10 x 9 x 8 x 7 = P(10,4) = 5040 possible slates, (b) (i) There are 3x9x8x7 = 1512 slates where a physician is nominated for president, (ii) The number of slates with exactly one physician appearing is 4 χ = 2520.
Of these, (b) 4 x 1 χ 3 x 2 = 24 are blue. By the rule of product there are (a) 4x12x3x2 = 288 distinct Buicks that can be manufactured. By the rule of product there are 5x5x5x5x5x5 = 56 license plates where the first two symbols are vowels and the last four are even digits. (c) The rule of sum in part (a) the rule of product in part (b). (b) Since there are eight Republicans and five Democrats, by the rule of product we have 8 x 5 = 40 possible pairs of opposing candidates. (a) By the rule of sum, there are 8 + 5 = 13 possibilities for the eventual winner. PARTI FUNDAMENTALS OF DISCRETE MATHEMATICSĬHAPTER 1 FUNDAMENTAL PRINCIPLES OF COUNTING Sections 1.1 and 1.2 1.
PART 4 MODERN APPLIED ALGEBRA 367 Chapter 14 Rings and Modular Arithmetic 369 Chapter 15 Boolean Algebra and Switching Functions 396 Chapter 16 Groups, Coding Theory, and Polya's Method of 413 Enumeration Chapter 17 Finite Fields and Combinatorial Designs 440 THE APPENDICES 459 Appendix 1 Exponential and Logarithmic Functions 461 Appendix 2 Properties of Matrices 464 Appendix 3 Countable and Uncountable Sets 468 TABLE OF CONTENTS PART 1 FUNDAMENTALS OF DISCRETE MATHEMATICS 1 Chapter 1 Fundamental Principles of Counting 3 Chapter 2 Fundamentals of Logic 26 Chapter 3 Set Theory 59 Chapter 4 Properties of the Integers: Mathematical Induction 95 Chapter 5 Relations and Functions 134 Chapter 6 Languages: Finite State Machines 167 Chapter 7 Relations: The Second Time Around 179 PART 2 FURTHER TOPICS IN ENUMERATION 207 Chapter 8 The Principle of Inclusion and Exclusion 209 Chapter 9 Generating Functions 229 Chapter 10 Recurrence Relations 243 PART3 GRAPH THEORY AND APPLICATIONS 285 Chapter 11 An Introduction to Graph Theory 287 Chapter 12 Trees 328 Chapter 13 Optimization and Matching 354 ISBN 0-2 12 3 4 5 6 CRS 06 05 04 03 PEARSON Addison Weslevĭedicated to the memory of Nellie and Glen (Fuzzy] Shidler No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Publishing as Pearson Addison-Wesley, 75 Arlington Street, Boston, MA 02116 All rights reserved. Reproduced by Pearson Addison-Wesley from electronic files supplied by the author. Grimaldi Rose-Hulman Institute of Technology PEARSON Addison Weslev Bostcn San Francisco New York London Toronto Sydney Tokyo Singapore Madrid Mexico City Munich Paris Cape Town Hong Kong Montreal
#Discrete mathematics ensley crawley 2.3 solutions manual
Instructor's Solutions Manual Discrete and Combinatorial Mathematics Fifth Edition Ralph P.