Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 6 - Section 6.6 - Generating Permutations and Combinations - Review Questions - Page 440: 7

Answer

a) If N objects are placed into k boxes, then there is at least one box containing at least [$\frac{N}{k}$]. b) There are at least 10 integers ending with the same digit.

Work Step by Step

a) If N objects are placed into k boxes, then there is at least one box containing at least [$\frac{N}{k}$]. b) According to the generalized pigeonhole principle, at least one box must contain [$\frac{91}{10}$]=10. .There are at least 10 integers ending with the same digit.
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