What is the greatest happiness principle in reference to euthanasia?

The greatest happiness principle, also known as the principle of utility, is an ethical theory that holds that the morally right action is the one that produces the greatest amount of good or happiness for the greatest number of people. In the context of euthanasia, the greatest happiness principle would suggest that euthanasia should be permitted under certain circumstances in order to achieve this good for the individual or group of people. For example, euthanasia could be permitted when a person is suffering from a terminal illness or in great pain and there is no other way to relieve their suffering, and where they have clearly expressed their wish for euthanasia. However, the greatest happiness principle does not always provide an easy answer, and there may be cases where the greatest good is unclear.