Question: A small business has 8 employees. Every day, the owner designates a team to do a certain task. The owner is careful never to designate a team that is a subset of a former team or a future team, because then some people might feel not really needed in some teams. Prove that even being so considerate, the owner can choose a different team on each of 70 consecutive days.

Brianna,

If every team was of the same size then no team could be a subset of another team. For example if every team consisted of 2 people then there would be 8 choose 2 which is

^8!/_{2! 6!} = 28

different teams and hence he could choose a different team for each of 28 consecutive days.

Penny