How do I make sense of combinations with repetition? I'm a non-math major but have to study a course in probability and statistics for graduate school. I was able to understand permutations with repetition and then permutations without repetition using examples, and then trying to generalize.
But I can't seem to find any examples of combinations with repetition that explain how the formula works, without going into multisets and things like that.
Help would be much appreciated.

I frame combinations-with-repetition problems as choosing/picking (order doesn't matter) $r$ items from $n$ categories (each category may be repeatedly picked).
For each selection, illustrate the $n$ categories using $(n-1)$ vertical bars as separators, then represent the $r$ selected items by filling $r$ stars in the according categories.
Notice that every selection contains $[(n-1)+r]$ positions filled by stars & bars, and that selections are distinguished by the $r$ stars filling in different combinations of positions (the vertical bars filling in the remaining positions).
Therefore, the total number of selections is the number of ways to choose $r$ positions from $[(n-1)+r]$ positions, i.e., $$\binom{n-1+r}{r}.$$
