The permissibility of men to greet women, and vice versa, is with the condition that there will be no fear of temptation to commit the unlawful. Here are the details:
1. A young woman is forbidden to greet men and to respond to their greeting.
2. A group of women or an old woman are allowed to greet men and to respond to men's greetings. Men are also allowed to greet a group of women or an old woman.
3. A man on his own is not allowed to greet a young woman.
4. A man on his own is allowed to greet a group of women.
However, in all these cases, Islamic rules in this regard, including the lowering of the gaze, are to be observed.