What are all of the possible 4 digit numeric combinations using 0-9?

Quick Answer

10,000

Long Answer

The numeric values 0-9 provide 10 total possibilities.

To expand this concept and understand how to arrive at the answer to this question in different situations read on...

If we assume a one digit combination, the possibilities as you already know are:

"0 1 2 3 4 5 6 7 8 9" for a total of 10.

If we assume a two digit combination the possibilities are 100, and here's why. Each of the possibilities in the above example with one digit, combine now with another ten possibilities for each. This is easier to understand visually:

0 1 3

______/\_______ ______/\_______ ______/\_______

| | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

While I only typed the first 3, this pattern is replicated for all the possibilities, in our case, all the numbers 0-9.

This pattern can be expressed verbally by, "total possibilities" to the power of "combination length" or in the formula:

X^n.

In this case the formula is 10^2. 10 because 0-9 is 10 possibilities and 2 because the length of our combination is 2.

Now let's assume that we have a 3 digit combination using numbers.

Formula:

10^3 = 1000 possibilities.