Math CentralQuandaries & Queries


Subject: number combinations
Name: Efrain
Who are you: Student

i want to know the different combinations for numbers 7 digits the number are 0-9 its basically the different phone number combinations
example: 555-6689 or 565-4896 i just want to know for many different combinations
are there.... thank you


If there were no restrictions on phone numbers other than the number of digits then you can argue as follows.

There are 10 choices for the first digit, any one of 0, 1, ..., 9. Whatever choice you make there are again 10 choices for the second digit. Thus there are 10 x 10 = 102 choices for the first two digits. Again whatever two digits you choose to start with there are 10 choices for the third digit and hence 10 x 10 x 10 = 103 choices for the first three digits.

Continuing there are 107 choices for a 7 digit phone number.

This is of course not correct as there are restrictions on the 7 digit combinations that form phone numbers. For example the first digit can't be 1, that indicates a long distance number.


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