Which Facebook App solution allows public figures and organizations to create a presence and connect with their audience?

The Facebook App solution that allows public figures and organizations to create a presence and connect with their audience is a Page. Pages are specifically designed for businesses, brands, celebrities, and organizations to offer a space where they can share information, engage with followers, and promote their products or services.

Pages have features that support content sharing, such as the ability to post updates, photos, and videos, as well as tools for running advertisements and analyzing audience engagement through insights. This distinct advantage makes Pages the ideal choice for building a public presence, as they provide the necessary tools for organizations and public figures to connect and interact with their audience effectively.

Groups, while also fostering community and interaction, are primarily designed for users to connect over shared interests rather than serve as a branding or outreach tool. Profiles are personal accounts meant for individual users, catering to friends and personal connections, but are not suitable for organizations or public figures. Events facilitate specific occasions but do not serve as a continuous online presence for organizations or public figures, therefore, they do not fulfill the purpose described in the question.