There is a train traveling on tracks. Ten people are tied down to the track you are on. You will be killing them if you choose to continue on this path. You have the ability to redirect the track, this will lead you to another track with only one person tied to the track. If you decide to take this path you will be killing that one person.
This is a famous dilemma that many ethical philosophers have tried to address.
In Jewish Law, the basic ruling is that numbers don’t decide the issue, and it is forbidden to murder one person even to save a number of people (deontological rather than consequential reasoning).
However, in the case of the train it is possible that one has the right to divert the train, because doing so is not a direct act of killing, but a direct act of saving a life, which later leads to killing the one person.
On account of this distinction, the Chazon Ish (Yoreh De’ah 69; Sanhedrin Chap. 25) has a doubt as to whether it is permitted or not.
Because this is a matter of doubt, later authorities write that one should not divert the train.
For instance, Rabbi Eliezer Waldenberg (Shut Tzitz Eliezer, Vol. 15, no. 70) concludes that in a similar case of worn brakes it is preferable to remain passive, even when a group of people will be killed, than to take the active step of killing others.
[For more on this subject, see our article here.]