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 - Exercise Set 11.1 - Page 693: 18



Work Step by Step

See page 690, The Fundamental Counting Principle: 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. --------- Each of the first three digits can be chosen in only one way. Ways of choosing the 4th digit ... 10 (any of the digits 0 - 9), 5th digit ... 10, 6th digit ... 10, 7th digit ... 10. Total codes possible (applying the Principle): 1$\times$1$\times$1$\times$10$\times$10$\times$10$\times$10$=10,000$ (This includes the number 699-0000. There are no constraints by which we should exclude it, so 10,000 remains as the answer)
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