The scenario you present is a classic ethical dilemma known as the "trolley problem," where individuals are forced to make a difficult decision that involves sacrificing one life to save many. There is no easy answer to this question, as it involves complex moral considerations and depends on various ethical frameworks. However, I will attempt to provide a detailed analysis of the two main perspectives on this issue.

1. Utilitarianism:
Utilitarianism is an ethical theory that focuses on maximizing overall happiness or well-being for the greatest number of people. From a utilitarian standpoint, sacrificing one life to save the group would be considered justifiable. This decision is based on the principle of maximizing overall welfare and minimizing harm. By sacrificing one person, the remaining 19 individuals are saved, potentially leading to a greater overall happiness.

One famous example related to this dilemma is the "fat man" variation of the trolley problem. In this scenario, a person can push a large man off a bridge to stop a runaway trolley from killing five people on the tracks below. From a utilitarian perspective, sacrificing one life to save five would be considered morally acceptable.

2. Deontology:
Deontology is an ethical theory that focuses on the inherent rightness or wrongness of actions, rather than the consequences. From a deontological standpoint, taking a life is inherently wrong, regardless of the outcome. Deontologists argue that certain moral principles, such as the prohibition against killing, should be upheld regardless of the consequences.

From a deontological perspective, sacrificing one person to save the group would be considered morally unjustifiable. Immanuel Kant, a prominent deontologist, argued that individuals have an inherent worth or dignity and should never be treated merely as a means to an end. Therefore, killing someone to save others would violate their intrinsic value and the principle of respect for persons.

In conclusion, the question of whether it is justifiable to take a life to save a group depends on the ethical framework one adopts. Utilitarianism would argue that sacrificing one life for the greater good is morally acceptable, while deontology would argue that taking a life is inherently wrong, regardless of the outcome. It is important to note that this is a highly debated topic, and different individuals may have diverse perspectives based on their personal values, cultural backgrounds, and ethical beliefs.