[Alt-text] Spongebob and Patrick work out their strategy with a utility based analysis.
We tend to assume that the means accomplish the ends, but that's not necessarily the case. The trolley problem never looks at where the trolley is going, just how it gets there. But if the way we want to get there doesn't actually go to the destination we want, then it's not a solution. Hope this helps. =D
edit: trolley is spelled with an e
To give an example of this, if someone wanted a peaceful nation state without violating privacy, but then accomplished peace through an invasive surveillance program they didn't actually accomplish their goal.
As long a person's goals aren't mutually exclusive like wanting to eat lots of ice cream and also never eating ice cream or violates physics like wanting more ice cream than there are atoms in the universe there is most likely a way to accomplish a person's goals. edit: typo
The first bit of that is exactly what I was trying to say, indeed almost exactly the same as an example I considered giving but didn't to avoid extra length, so we're in agreement there.
The second, though, I think misses that there is a distinction between physical possibility and practical ability. In theory, it breaks no physical laws for me to become richer than Jeff Bezos by the end of next year. In practice, though, the fact that most pathways to achieving that level of wealth, especially quickly, involve a whole lot of luck on very low likelihood (but not impossible events), means that there is probably no sequence of actions that I can actively decide to take that stand any reasonable chance of me achieving it. There are technically sequences like "buy a lot of winning lottery tickets in a row" that might do it, but because they rely on abilities I don't have (like knowing which tickets win in advance), I can't actually attempt to take those paths.
Becoming richer than Jeff Bezos most likely requires you to have been born in a very wealthy family, so your odds are practically zero.
There are definitely goals that are statistically improbable that are beyond are current means to navigate consistently, like getting rich through lottery tickets, but they don't violate physics. We do have to take into account what we are able to influence, practically speaking, with our actions.
I bring up physics because we live in a physics-based universe as opposed to a moral universe. So our analysis of our course of actions must take that physical reality into account when pursuing a subjective moral outcome. If we lived in a moral universe, like D&D, we would only need to ask do the ends justify the means. Acting to achieve a goal in a such a universe would, in theory, always be a matter of acting in a way that was consistent with the end goal. But that's not the universe we live in.