Let G(V, E) be a directed graph, where V = {1, 2,3, 4,5} is the set of…

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.

$A[i][j] = \begin{cases}1 & \text{if } 1 \leq j \leq i \leq 5 \\0 & \text{otherwise}\end{cases}$

𝐴[𝑖][𝑗] = 1 indicates a directed edge from node i to node j. A directed spanning tree of G, rooted at r ∈ 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_____________.