Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 11 - Counting Methods and Probability Theory - 11.1 The Fundamental Counting Principle - Concept and Vocabulary Check: 4

Answer

True.

Work Step by Step

The number of ways in which a series of successive things can occur is found by multiplying the number of ways in which each thing can occur. ---------- Say the current number of telephone numbers is N. Adding a new digit to each telephone number, (which can be chosen from 0-9, that is, in 10 ways), by the Fundamental Counting Principle, the total number of newly formed numbers is $N\times 10.$ So when population increases, we increase the number of phone numbers tenfold by adding a digit to each phone number. And, if needed, when population reaches this number, we increase the number of phone numbers tenfold again, by adding another digit. And so on. We can accommodate the rise in population by adding digits to the phone numbers. The statement is true.
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