Number of distinct cycles of length 4 in a complete graph of 6 labelled vertices. [closed]

Question

This is in reference to the below question

https://gateoverflow.in/473/gate2012-38

My doubt here is

In this question, we can also solve like first we select 4 vertices out of 6 in 6C4 ways.
Now we need to count how many cycles we can form with 4 vertices.And I think this is same as number of Hamiltonian circuits we can form in K4(Complete graph of 4 vertices)
so this is (n-1)! /2 which evaluates to 3 in case of n=4.So by multiplication rule, total cycles we have 45.Is this way correct?
 

Comments

Correct.