How many unique words starting with a can be obtained from given m a's and n b's?

Question

I am stuck at this questions while trying to understand permutations. How would I get number of unique words and how can I know they all start with a.

I am not able to understand how we proceed in this question, still I did something like this:

I fixed one 'a' from m a's in the starting of the word. I have now m-1 a's and n b's.

Now how do we get the number of words and also ensure that they are unique.

Answer 1

Use stars and bars: you have $m$ places to put $n$ $b$'s.

So, ${n+m-1\choose n}$.

I'm using theorem two.