GATE 2022
Let G(V,E) be a directed graph, where V = {1,2,3,4,5} is the set of vertices and E is the set of directed edges, as defined by the following adjacency matrix A.
A[i][j] = 1, if 1 ≤ j ≤ i ≤ 5; A[i][j] = 0, otherwise
A[i][j] = 1 indicates a directed edge from node i to node j. A directed spanning tree of G, rooted at r in V, is defined as a subgraph T of G such that the undirected version of T is a tree, and T contains a directed path from r to every other vertex in V. The number of such directed spanning trees rooted at vertex 5 is_____________.