Having only digits $1,2,3$. How many $10$-digit numbers can you make with these digits such that you do not use 1 at all? ($2^{10}$?)
How many $10$-digit numbers can you make with these digits provided you use $1$ twice? ($2^8$?)
Having only digits $1,2,3$. How many $10$-digit numbers can you make with these digits such that you do not use 1 at all? ($2^{10}$?)
How many $10$-digit numbers can you make with these digits provided you use $1$ twice? ($2^8$?)
Your answer to the first question is correct.
In the second question you have to think about places where two 1's will stand. You can choose this in $\binom{10}{2}$ ways.
Hint: For the second question (the first seems to be clear). Did you take into account that the two 1's can be at different positions?