How many are the possible outcomes from throwing $n$ (identical) dice.
I know it is a combination with repetition, but don't really know how to apply the formula.
I need an explanatory answer with the process of thinking.
The book's solution:
$$\binom{n + 5}{5}$$
Best Answer
A common way to explain it is known as "stars and bars".
I shall illustrate it putting identical balls into distinct bins ($1-6$) depicting the results obtained
One result with $n= 10$, say, would be $\;\;\bullet|\bullet|\bullet|\bullet\bullet\bullet\bullet|\bullet |\bullet\bullet\;\;$
Make two notes: only $5$ dividers are needed to depict $6$ bins, and you could have $0$ balls in some bins, e.g. $||\bullet\bullet\bullet\bullet|\bullet\bullet\bullet|\bullet\bullet\bullet|$ depicting $0-0-4-3-3-0$
So if there are $n$ balls and $k$ bins ($k-1$ dividers), the only choice you have is to place the dividers among the lot, thus
$\dbinom{n+k-1}{k-1}$ which works out to $\dbinom{n+5}{5}$ for your particular example.
You could profitably look here to have a more detailed explanation