Consider a complete graph with 6 vertices labeled A, B, ... F. (a) If you can start at any vertex, how many Hamiltonian circuits exist? (b) If you can start at any vertex, how many different Hamiltonian circuits exist if a circuit and its mirror image are not counted as separate circuits? (c) If you start at vertex B, how many different Hamiltonian circuits exist if a circuit and its mirror image are not counted as separate circuits?

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