Permutations . . . (4 x 3 x 2 x 1) = 24 of them
Combonations . . . only 1 of them
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well the first 9 digit number is 100 million 100,000,000 the last 9 digit number is 999 million 999,999,999 just minus the two numbers and you get... 899,999,999 so there are around 900 million 9 digit numbers.
An on-line prime number chart ended at 10007. There are many more charts available for download. So the answer is that there are many five digit prime numbers.
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.
If the first digit is 9, you have 9 options (0-8) for the second digit. If the first digit is 8, you have 8 options (0-7) for the second digit. Etc. This leaves you with the arithmetic series: 0 + 1 + 2 + 3 + ... + 9.