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

Simplify it to two numbers. That answer isn’t 99, it’s 2, which is equal to 2!(two factorial, which is 2 times 1). Then three numbers, it’s not 999, it’s 3!, 3x2x1 which is 6. Four unique digits (or characters) can be arranged 4! ways. In the first place we have 4 uniques to pick from, then in the second place we have 3 uniques, third place we have 2 to pick from and the last place leaves us one option. That’s 4x3x2x1, or 4! or 24.