Little math problem(s) October 2020

[pier4r]

I still have a lot to catch up, but if I guess I can add a couple of contributios even if I missed a lot in the last years.

Months ago, before Covid 19, I got in the metro. After few stations a colleague entered the train and sat directly beside me and we didn't recognize each other until we were at the station near to work. I was busy reading and he too.

Then I thought: what are the odds that we sit, without noticing each other, near to each other?

Given that:
- train schedule is a train every 5 minutes (between stations the train use 2 minutes, when there are no problems)
- period of time where we can pick the train is like 2 hours (from 7 to 9 AM)
- my station is 5 or 6 stations before his (he takes sometime one, sometime the other)
- we work around 275 days a year, say 240 to avoid holidays/sickness (and I do not include those times where I take the bike)
- a train has 8 cars (let's assume that entering a different car means sitting away, although some trains have a lot of cars connected)
- Using an average train (it depends on which type of car is used), per car there are 48 places (sitting).