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It is widely acknowledged that transparency of automated decision making is crucial for deployability of intelligent systems, and explaining the reasons why some decisions are "good" and some are not is a way to achieving this transparency. We consider two variants of decision making, where "good" decisions amount to alternatives (i) meeting "most" goals, and (ii) meeting "most preferred" goals. We then define, for each variant and notion of "goodness" (corresponding to a number of existing notions in the literature), explanations in two formats, for justifying the selection of an alternative to audiences with differing needs and competences: lean explanations, in terms of goals satisfied and, for some notions of "goodness", alternative decisions, and argumentative explanations, reflecting the decision process leading to the selection, while corresponding to the lean explanations. To define argumentative explanations, we use assumption-based argumentation (ABA), a well-known form of structured argumentation. Specifically, we define ABA frameworks such that "good" decisions are admissible ABA arguments and draw argumentative explanations from dispute trees sanctioning this admissibility. Finally, we instantiate our overall framework for explainable decision-making to accommodate connections between goals and decisions in terms of decision graphs incorporating defeasible and non-defeasible information.