Suppose there exists a Facebook group of n profiles, where n > 2. Within this group, there are some friendship connections. A member of the group could be friends with any other member, or none at...

Extracted text: Suppose there exists a Facebook group of n profiles, where n > 2. Within this group, there are some friendship connections. A member of the group could be friends with any other member, or none at all. Prove that, no matter how these friendships are distributed, there will be at least two members with the same number of friends.