Question

Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to 

(A) 15 

(B) 30 

(C) 90 

(D) 360

Answer 1

(C) 90

4 vertices from 6 vertices can be chosen in in ⁶C₄ ways and number of ways in which 4 vertices can be arranged In a cycle Is ( 4-1)! , so total number of 4 length cycles are ⁶C₄ .3! = 90