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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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