The Group Option is Grayed Out
This happens when you are trying to group placeholders on a slide with other slide objects. Placeholders are special objects on a slide that are part of the slide layout. For example in a conventional bulleted slide, the title and text box are often placeholders, and these cannot be grouped with other inserted slide objects like shapes, pictures, or charts. That's the reason your Group option may be grayed out.
It's also found that if you use the Photo Album option to create slides with imported pictures, then you cannot group them with pictures inserted using the Insert menu of tab options.