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 6.1 - The Basics of Counting - Exercises - Page 398: 57

Answer

54$\times$ $65^{65534}$ number of variable names possible

Work Step by Step

First digit can be selected in 26 + 26 + 1 + 1 = 54 (uppercase + lowercase + dollar + underscore) All other digits can be selected in 26 + 26 + 1 + 1 + 10 + 1 = 65 (Uppercase + lowercase + dollar + underscore + numbers + no value) so total number of variable names = $65^{65534}$$\times$54
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