What's the difference between a permutation and a combination with repetition? My understanding is that a permutation is used to find the number of rearrangements of different elements, taking into account possible orders. A combination is used to find the number of rearrangements of different elements leaving out order.
If you have a combination with repetition, isn't that the same thing as a permutation? What exactly is being repeated?
I was hoping someone could clear this up for me.  Thanks.

In a permutation you have only one each of the available elements.  So if you are taking permutations of three elements out of $\{1,2,3,4\}$ some of the legal ones are $(1,2,3), (3,1,4), \text {and} (2,3,1)$.  There are a total of $24$ of them.  As you say, combinations do not care about order.  There are only four taking combinations of three out of the same set: $\{1,2,3\},\{1,2,4\},\{1,3,4\},\{2,3,4\}$.  Combinations with repetition would allow multiples, so $\{1,2,2\}$ becomes legal, but is still the same as $\{2,1,2\}$.  These are called multisets.
