There are 900 possible three-digit numbers not beginning with 0. (Note, however, that this question does not accurately describe the restrictions on numbers that can be used as area codes.)
If you include 0000, ten thousand unique four digit codes are possible.
There can be 103 = 1000 codes.
The first digit has 4 choices for its digit. The second digit has 6 choices and the third has 3. The solution would simply be 4*6*3=72 three digit numbers.
yes of course I know people with 3 and 2 digit addresses
If the first digit can be zero, there are 5,040. If the first digit can't be zero, there are only 4,536.
If you include 0000, ten thousand unique four digit codes are possible.
There can be 103 = 1000 codes.
100,000 - Every number from 00000 to 99999.
There are 210 4 digit combinations and 5040 different 4 digit codes.
With the restrictions specified in your question, there are 8 x 2 x 10 = 160 possible area codes. However, those restrictions do not match the restrictions on actual area codes in North America (USA, Canada, etc.). North American area codes have the first digit not 0 or 1, the second digit not 9, and the third digit not the same as the second digit (such codes are reserved for special purposes like toll-free), leaving 8 x 9 x 9 = 648 possible area codes.
The first digit has 4 choices for its digit. The second digit has 6 choices and the third has 3. The solution would simply be 4*6*3=72 three digit numbers.
450
The number of 3-digit numbers with no repeated digits is simply 10x9x8 = 720, if you allow, for example, 012 as a 3-digit number. There are 10 digits, any of which might be the first digit. The second digit can be any digit except the digit that was used for the first digit, leaving 9 possibilities. The third digit then has 8 possibilities, since it can't be the same as the first or second digit. The actual number of possible area codes will be lower, because there are additional restrictions on the number combinations for a valid area code. For example, in North America (USA, Canada, etc.), the first digit of an area code cannot be 0 or 1 and the middle digit cannot be 9.
yes of course I know people with 3 and 2 digit addresses
If the first digit can be zero, there are 5,040. If the first digit can't be zero, there are only 4,536.
There are 26 choices for the first letter, 25 choices for the second letter (since we can't repeat the first letter), and 10 choices for the digit. Therefore, the total number of possible codes is: 26 x 25 x 10 = 6,500 So there are 6,500 possible codes with 2 letters and one digit if no letter or digit appears more than once.
Assuming that the first digit of the 4 digit number cannot be 0, then there are 9 possible digits for the first of the four. Also assuming that each digit does not need to be unique, then the next three digits of the four can have 10 possible for each. That results in 9x10x10x10 = 9000 possible 4 digit numbers. If, however, you can not use the same number twice in completing the 4 digit number, and the first digit cannot be 0, then the result is 9x9x8x7 = 4536 possible 4 digit numbers. If the 4 digit number can start with 0, then there are 10,000 possible 4 digit numbers. If the 4 digit number can start with 0, and you cannot use any number twice, then the result is 10x9x8x7 = 5040 possilbe 4 digit numbers.