Find the number of $x$ digit numbers in base $n$

Question

I tried to understand this but I can't. It is confusing and I even don't know what the question mean. Help me out, Thanks!

The number of $x$-digit numbers in base $n$ is
(a) $n^x$ (b) $n^x-1$ (c) $n^x-n$ (d) $n^x-n^{x-1}$

Answer 1

Let's say you have some $x$-digit number. If we are free to choose any digits, there will be exactly $n^x$ numbers that you can express with these digits, but the numbers will not be unique as numbers, since $012 = 12$. So it we want to count all the numbers we can make with $x$ digits, we would need to disregard all the options where the leading number is $0$. But this leaves us with $n^{x-1}$ choices to remove!

So the answer is (d).