Binary numbers with at most

Question

I am trying to find how many binary numbers are there with $10$ digits if the first two must be $1$s.

I am thinking this to be $2^{10 - 2}$, but I'm not sure.

Answer 1

This is like the same problem as creating a $8$ digit number, then attaching two $1$s in front of it. Therefore, our answer is: $$2^8=\boxed{256}$$