That's a great way of doing it. My way of remembering it is, "How many ways can you divide 2017 pieces of candy among 3 children?" Where this is a combination problem. The little tricks are in making sure you choose 1 less arrangement, for example, you only need to choose 2, and you need 2019 items (candy + children - 1). So 2019 choose 2 is also the answer.
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Yes, that's the same problem. Just as with the kids and candy, order is important here; the number partition problem can be done as permutations or combinations, depending on the problem.