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Probability calculation of dependent events with limitations


New member
Oct 15, 2019
Dear forum,

First time posting and as English is not my native language, I'd like to apologize in advance for any linguistic errors I make.
Yesterday, I received a case which sounded really easy to calculate but for some reason I can't get my head around it.
This is the case:
In a shipping company for clothes there are 10 different orders being handled at the same time. These orders all have 4 clothes, which means there are 40 clothes in total that have to be sorted. At random these clothes are being picked from the stock and assigned to an order. The issue is, that there are only 6 order locations (packing and shipping), while there are 10 orders to be picked. But, when 4 clothes are assigned to 1 order location, the order is complete (packed and shipped) and will open up again for a new order order. How do I calculate the probability that the whole production line will halt since the 7th order is being picked while there are only 6 locations.
It seems to me that there is a calculation for this but I just can't grasp it at the moment. I really do apologize if this is a basic question and if my brain just doesn't want to co-operate but for now I really have no clue how to get this to work.

If you have any other questions regarding the case or think you have some information that might help me out. Please let me know.

Thank you in advance.