Is it OK to push the fat guy? To me, it depends on the perspective. If I am just an onlooker, I won't push the guy, as I am not responsible for otherwise killing the 5. Killing one person vs. not saving 5 persons have greatly different psychological effect on me. But if I am the driver of the trolley car and I have the option of turning the steering to open a trap door to drop the fat guy, yeah, I will do it. For the driver, the options are killing one or killing five, while for the onlooker, the options are killing one or not saving five. There is a huge psychological distinction.
Is it OK to kill the cabin boy? No, I won't do it, but I am OK with lottery idea.