# Join In the Party

How many ways are there for 5 people to be friends with each other on Facebook, such that each person is friends with at least 1 other person in the group.

Details and assumptions

Facebook friendship is mutual. If $$A$$ is friends with $$B$$, then $$B$$ is friends with $$A$$.

2 ways are considered distinct, if the status of friendship between 2 people changed. For example, if $$A$$ and $$B$$ are friends, and $$C, D, E$$ are all friends with each other, then this is a different way from if $$A$$ and $$E$$ are friends, and $$B, C, D$$ are all friends with each other.

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