How many whole numbers is there that have at most 10 digits and that can be written using only the digits 0 and 1?

Answer 1

This sounds like you're asking about a 10-digit binary number.

Each position has two possibilities. For every position, you add a power of two.

So 10 positions = 2^10 = 1024 possibilities.

To show you how it works, I will demonstrate with a 3-digit binary number.

000
001
010
011
100
101
110
111

As you can see, there are eight (8) possibilities with three binary digits.

3 positions = 2^3 = 8.