My answer: Write a little program to simulate it

Brendon Greeff writes:

I was searching for an online math blog and found your email address. I have a question relating to the draw for a sports tournament.

If there are 20 teams in a tournament divided into 4 groups, and those teams are selected based on four “bands” (Band: 1-5 ranked teams, 6-10, 11-15, 16-20), ie. the top 5 ranked teams are first drawn randomly into the 4 groups, then teams ranked 6-10 drawn are drawn randomly, and so on and so forth.

If all the teams are the same for 2 consecutive tournaments, what are the chances/ odds/ probability that 3 teams from Bands 1, 2 and 3 would end up in the same group for 2 consecutive tournaments?

My response is given in the title above. You can do the simulation in R, Python, whatever. The point is that, if you want to do probability and statistics, it’s as important to know some programming as it is to know some math. (And that’s relevant to our discussion from the other day.)

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