# Probability that a permutations is going to reoccur

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!

• This is a variant of the birthday problem. The median number of days needed (in a uniform random setting) is about 31 or 32, actually! May 14 at 6:11
• 1. How do you determine who starts ? 2. Do people have to randomly choose their throw considering only those people who have not yet got the ball ? 3. If not, when does the experiment for the day stop ? May 14 at 7:09
• @trueblueanil 1. We also choose random, a "Who would like to start?" is asked at the beginning. 2. Yes, so everyone has his/her turn, it wouldn´t make sense to throw the ball to someone who has already gotten it. 3. It stops when each one has got his turn, so it is a recap meeting, where everyone just recaps what he has done. May 14 at 7:26
• @GregMartin thanks for the reply, could you elaborate a bit on the formula or is it just the birthday problem formula? May 14 at 7:26