Problem #PRU-100590

Problem

Problems often involve a protagonist, a quest and a story. In combinatorics, stories can help us prove identities and formulas, that would be difficult to prove otherwise. Here, you can write your own story, which will show that the following statement is always true:

The number of ways we can choose $k$ out of $n$ items is equal to the number of ways we can choose $k$ out of $n-1$ objects PLUS the number of ways in which we can choose $k-1$ out of $n-1$ objects.