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: 6

Answer

a) The pigeonhole principle states that if n pigeons are to go into m holes, such that n>m, then at least one hole must have more than one pigeon. b) At least 2 number ends with the same digit.

Work Step by Step

a) The pigeonhole principle states that if n pigeons are to go into m holes, such that n>m, then at least one hole must have more than one pigeon. b) The last digit of any number has to one of these 10: 0,1,2,3,4,5,6,7,8,9. So if we match 11 numbers then at least 2 of them must have the same last digit.
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