The telephone company wants to know how many different phone numbers are available for one area code. the only restrictions are on the prefixes, you can't start with a zero and you can't use 411, 611, 811, 911, or 555. how many different phone numbers are available?
phone numbers have to be seven digits, right? 8*9^6
now the three digit phone numbers are not really phone numbers, as they are three digit shortcuts.
In North America, a typical phone number has a 3 digit area code, then a 3 digit number, than a 4 digit number.
e.g. 123 - 456 - 7894
By the "prefix" do you mean the 3 digit number in the middle?
I will assume that.
So number of possible prefixes without restrictions:
= 9x10x10x= 900
excluding the 5 listed above leaves us with 895 possible prefixes.
for each of those, the remaining 4 digit numbers could be 10x10x10x10 = 10,000
So for a given area code, the number of permissible phone numbers
= 895x10000 = 8,950,000
To calculate the number of different phone numbers available for a given area code, we need to consider the restrictions on the prefixes.
First, let's determine the total number of possible prefixes. Assuming we have a ten-digit phone number with a three-digit area code, the first digit can be any number from 1 to 9 (since we can't start with zero), which gives us 9 possibilities. The second and third digits can be any number from 0 to 9, giving us 10 possibilities for each digit.
Therefore, the total number of possible prefixes is: 9 (for the first digit) × 10 (for the second digit) × 10 (for the third digit) = 900.
Now, let's consider the restricted prefixes. We cannot use 411, 611, 811, 911, or 555. Since each of these prefixes has one specific combination, we subtract them from the total count.
So, the number of restricted prefixes is 5.
Finally, subtract the restricted prefixes from the total count of possible prefixes to get the number of different phone numbers available:
Number of different phone numbers = Total count of possible prefixes - Number of restricted prefixes
Number of different phone numbers = 900 - 5
Number of different phone numbers = 895
Therefore, there are 895 different phone numbers available for the given area code, considering the restrictions on the prefixes.