Self doubt

Question

How many simple directed (unweighted) graphs on the set of vertices {v0,v1,…v5} are there that have at most one edge between any pair of vertices? (That is, for two vertices a, b, only at most one of the edges (a, b) and (b, a) is in the graph.)

Answer 1

between any pair of vertices we can have atmost one edge that means we have 3 possibilities 

let verices pair is (u,v)

1. No edge between u and v
2. Edge from u to v
3. Edge from v to u 

so no of pairs in 6 vertices graph = 6C2 

and each pair have 3 possibilities so no. of graphs possible = 3^(6C2)= 3^15