I hated math but I remember this mathematical problem, do you know the answer?

If there were a 4 digit number using any combination of the numbers 0-9, HOW MANY POSSIBLE COMBINATIONS WOULD THERE BE? For example the last four digits of the social security numbers, how many numbers are possible there and how do you compute it? I had several ideas but thought surely someone knows exactly how to do this correctly…what better place then here to ask?

10,000…the numbers from 0 to 9,999.

According to this page, there are 10,000 combinations. Reasoning given.

10 possibilities for each digit, four digits total, gives you 101010*10 or 10[sup]4[/sup] or 10,000.

And, for completeness, if your combos also include letters, the number of possibilities is 363636*36, or 36^4, or just short of 1.7 million.

The “why” is 10 numbers (0-9) plus 26 letters (a-z).

If you allow mixed case, the choices become 0-9 plus a-z plus A-Z, (10+26+26) – 62^4 = just under 14.8 million combinations.

10,000 makes sense…I thought so but had another person tell me that was not correct. Thanks :slight_smile:

One could argue that the answer is 9999, but that’s if you forget (or exclude) 0.

Although the person making that argument doesn’t really have a leg to stand on…