How many ways are there to distribute $k+n$ identical photocopies to $n$ students so that each student receives at least one
Let $n$ be the number of students and $k+n$ be the number of photocopies.

We start by distributing one photocopy to each student.

Then, we need to distribute the remaining $k$ photocopies to $n$ students in any way.

Let's denote the photocopies by circles and draw $n-1$ lines.

The number of circles between two lines then corresponds to a student.

[Draw diagram]

Therefore, we need to choose $n-1$ lines from a total of $k+(n-1)$ points or lines.

We finally obtain

$$
\binom{n+k-1}{n-1}
$$

possibilities.