Heavy counting of routes
Source: Bulgaria JBMO TST 2023, Day 3, Problem 2
June 17, 2023
countingcombinatorics
Problem Statement
On the coast of a circular island there are eight different cities. Initially there are no routes between the cities. We have to construct five straight two-way routes, which do not intersect, so that from each city there are one or two routes. In how many ways can this happen?