20 cities, how many ways to build 187 roads Question:
There are 20 cities in the country. The government allocated money for the construction of 187 roads. Each road connects two different cities and does not pass through other cities. There cannot be more than one road between any two cities. How many ways are there to build roads?
Attempt
This is a graph with 20 vertices, 187 edges and no multi-edges. There are $187 \choose 2$ ways to plot 187 edges, which is 17391. However that's not the right answer and I'm not sure where I'm going wrong with my reasoning.

There are $\binom{20}{2}$ possible roads, we must select $187$ of those to build. The number of ways to do this is $$\binom{ \binom{20}{2}}{187}$$.
