Hamiltonian cycles

Question

Number of distinct Hamiltonian cycles are there in a unlabeled complete graph K6______ [Note : the path a->b->c is same as b->c->a]

Answer 1

HC condition is each vertex should have atleast degree=2.

for complete graph the number of unorderd hamiltonian cycle = number of ways you can arrange unlabelled vertex= 6!/6=120

Comments

It should $\frac{n!}{2*n}$ . Divide by 2 because abc is same as acb (cycle in reverse direction)?