Question 1176885
Here's how to determine the maximum number of edges in a simple, connected graph with 20 vertices:

**Understanding the Concept**

* A simple graph means no loops (edges connecting a vertex to itself) and no multiple edges (more than one edge between the same pair of vertices).
* To maximize the number of edges, we want every vertex to be connected to every other vertex. This is called a complete graph.

**Formula for Complete Graphs**

The number of edges in a complete graph with 'n' vertices is given by the formula:

* Edges = n(n - 1) / 2

**Applying the Formula**

In our case, n = 20. So, the maximum number of edges is:

* Edges = 20(20 - 1) / 2
* Edges = 20(19) / 2
* Edges = 380 / 2
* Edges = 190

**Answer**

The maximum number of edges a simple, connected graph with 20 vertices can have is 190.