Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 12 - Counting and Probability - Chapter Review - Review Exercises - Page 888: 17

Answer

$1,600,000$

Work Step by Step

The generalized basic counting principle says that if an event $e_1$ can be performed in $n_1$ ways and an event $e_2$ can be performed in $n_2$ ways, then there are $n_1n_2$ ways of performing them together. This can easily be extended to $n$ events. Here, we have $8$ choices for the first digit (all digits apart from $0$ and $9$), $2$ choices for the last digit ($2$ or $3$) and $10$ choices (all digits) for the rest of the $5$ middle digits. Thus, using the generalized basic counting principle, the total number of phone numbers is: $8(10)(10)(10)(10)(10)(2)=1,600,000$
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