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Concept explainers
Telephone Numbers Using the digits 0, 1, 2,...,9, how many 7-digit numbers can be formed if the first digit cannot be 0 or 9 and if the last digit is greater than or equal to 2 and less than or equal to 3? Repeated digits are allowed.
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To find: How many seven digits can be formed?
Answer to Problem 17RE
1600000
Explanation of Solution
Given:
Using the digits 0, 1, 2, … 9, 7-digit numbers has to be formed if the first digit cannot be 0 or 9 and if the last digit is greater than or equal to 2 and less than or equal to 3? Repeated digits are allowed.
Calculation:
The generalized basic principle of counting.
we need to choose 7 digit number using 0, 1, 2 …9.
First digit cannot be 0 or 9.
Hence number of choices for 1st digit .
Number of choices for each 2nd, 3,rd, 4th, 5th and 6th digit is 10.
Last digit is greater than or equal to 2 and less than or equal to 3.
Hence last digit can either be 2 or 3 only.
The number of options for last digit is 2.
Therefore the number of options for 7 digits is .
Chapter 13 Solutions
Precalculus Enhanced with Graphing Utilities
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