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.

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Answer 1

Combinations is the important bit here

You’re not saying “how many 8 digit numbers are there”, you’re being asked “how many different ways are there to arrange 8 different numbers”.

Change it to letters instead to make it clearer so you don’t think of it as a big number. You have the letters A, B, C, D, E, F, G, and H. How many different combinations can you make that have one and only one of each letter? ABCDEFGH is valid, so is BADCFEHG but AAAAHHHH is not valid because it isn’t a combination of all 8

For the first spot you can pick from any of the 8, for the second slot you can only pick from the *remaining* 7 letters, the third slot is 6 *remaining*, and so on. The final number of combinations is 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320