Respuesta :
Answer:
The required answer is: [tex]9^7\times 10^3[/tex] or 4782969000.
Step-by-step explanation:
Consider the provided information.
All telephone numbers are 10 digits long, consisting of a 3-digit area code, then a 3-digit "exchange" number, followed by a 4-digit number.
The numbers are: 0, 1, 2, 3, 4, 5, 6, 7 ,8, and 9
It is given that no 0 is allow in area code, so for area code we can select 9 numbers out of 10 numbers. i.e 1, 2, 3, 4, 5, 6, 7, 8, and 9
We have 9 numbers for each 3-digit area code,
Area code: 9×9×9 = 9³
no 9 in the final 4-digit number, so for 4-digit code we can select 9 numbers out of 10 numbers. i.e 0, 1, 2, 3, 4, 5, 6, 7, and 8
4-digit number: 9×9×9×9 = [tex]9^4[/tex]
The exchange number can be any number so for exchange number we can select 10 number. i.e 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9
Exchange number: 10×10×10 = 10³
Thus, the total number of possible phone numbers will be:
[tex]9^3\times 9^4 \times 10^3[/tex]
[tex]9^7 \times 10^3[/tex]
[tex]4782969000[/tex]
Hence, the required answer is: [tex]9^7 \times 10^3[/tex] or 4782969000.
