If I’m trying to find the number of unique different combinations for 8 numbers why isn’t the answer all 99999999 excluding all zero.

Question

I think the number is 40,320.

Edit: Background…For work we need to create a unique code for fraud detection and the code can be no longer than 8 numerical digits. The generation of this number is another story. This is just for my own understanding.

In: 0

Answer 1

99999999 is the correct answer if you include 0 as a number that can be used. For example if the number ’20’ is written as an 8 digit number it’s ‘00000020’. This gets included in your example because it’s not a string of all 0’s.

0-9 gives you 10 possible numbers to use.

If they can be used multiple times, then for 8 digits you have 10^8 combinations. 10 choices for the first digit, 10 for the second… all the way to the 8th digit.

That gives you 100000000 combinations, if you exclude ‘00000000’ then you are left with 99999999 combinations.