A telephone number consists of seven digits with the restriction that the first digit cannot be 0

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A telephone number consists of seven digits with the restriction that the first digit cannot be 0 or 1. Repetition of digits is permitted.

(a) How many distinct telephone numbers are possible?

(b) How many distinct telephone numbers are possible with three-digit area codes preceding the seven-digit number, where the first digit of the area code is not 0 or 1? 

(c) With the increasing use of cell phones and paging systems, our society is beginning to run out of usable phone numbers. Various phone companies are developing phone numbers that use 8 digits instead of 7. How many distinct phone numbers can be made using a three digit area code followed by an eight digit phone number, where the first digit of the area code and the phone number cannot be 0 or 1?

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A Survey of Mathematics with Applications

ISBN: 978-0134112107

10th edition

Authors: Allen R. Angel, Christine D. Abbott, Dennis Runde

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