2019 Fall Team #2
Source:
April 17, 2022
combinatorics
Problem Statement
Alex, Bob, Charlie, Daniel, and Ethan are five classmates. Some pairs of them are friends. How many possible ways are there for them to be friends such that everyone has at least one friend, and such that there is exactly one loop of friends among the five classmates?
Note: friendship is two-way, so if person x is friends with person y then person y is friends with person .