Is it permissible in Islamic law for a man aged 83, whose wife has passed away and whose children are married, to hire a 39-year-old widow with children to do housework and prepare food in the morning, while they are alone in the house?

It is not permissible for a man to be in seclusion with a non-mahram (definition) woman, even if he is old, due to the generality of the Prophet's saying, peace and blessings be upon him: "No man is to be in seclusion with a woman except with a mahram." An exception to this is if the man is decrepit—very old, with his mind altered and his desire ceased—and in need of someone to serve him. In such a case, his seclusion with a woman is permissible, whether she is young or elderly. It is preferable, however, that some of her children be present with her to avoid suspicion.