Still incorrect.
1 bit: 2 ways.
2 bits: 4 ways.
3 bits: 8 ways.
4 bits: 16 ways.
What is this pattern?
Because if I have 2 ways of doing one thing, and 3 ways of doing another, I don't have 5 ways of doing them both, I have 6. Think of it this way: for each way of doing the first thing, I have 3 ways of doing the second. Therefore, there must be 6 ways to do them both.
Because the code of the shop consists of 10 digits. Let's look at it another way.
_ _ _ _ _ _ _ _ _ _
Ok, I put 10 blanks. In each blank, you can put 2 digits, that is either 0 or 1.
In the first blank, you have two choices, in the second, again two choices, in the third, again two choices, etc.
This gives: $\displaystyle 2\times2\times2\times2\times2\times2\times2\times2 \times2\times2 = 2^{10} = 1024$