In a committee of 360 people, each member belongs to exactly three subcommittees, and each subcommittee has exactly 6 members. Determine the number of subcommittees.
Let $X$ be the set of pairs $(m, s)$ where $m$ is a member and $s$ is a subcommittee. Denote $k$ as the number of subcommittees. We have $|X|=6k=3 \times 360$ thus $k=180$.