I know that to solve this I have to figure out how many total possible edges there are However, I am unsure how to do this ? Once I am able to figure out the number of edges, I can choose 15 out of the total possible edges and find out the answer but I am stuck, can anyone explain to me how to figure that out?
2026-05-14 17:50:40.1778781040
How many graphs on the vertex set {1, ..., 12} have exactly 15 edges?
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Based on the comments, the graph in question is an undirected simple graph (a graph where edges are uniquely determined by the set of their endpoints). This is the most common type of graph studied in graph theory. There are $\binom{12}{2}=\frac{12(11)}{2}=66$ possible edges and we want exactly 15, so the answer is $$\binom{66}{15}$$ which is incidentially also known as $$268367258592576$$