So I´m doing an experiment on my own, without telling my team to increase randomness. We meet everyday for a quick recap session, where everyone can "throw the ball" to anyone of their desire.
What I am doing is that I am keeping a record of the permutation for each day (e.g., A-C-F-D-B-E). We are a team of 6, and until now, after 30 days, no permutation has been repeated yet.
My question: after how many days can I expect a reoccurance of a permutation (the exact permutation does not matter, it must simply be the same as one of the previous permutations)? Is this a similar problem to the birthday problem?
Would be fun if I could get a theoretical answer and test it in practice. Thanks in advance!