Math Is Fun Forum

Landlord

Member

Registered: 2008-07-29

Posts: 1

what are the odds? ( probabilities )

Hey mighty brains out there, this is a real life case scenario with which I need some help . 31 people need to share a place that would comfortably take 6 per night. All 31 people will not need the place the same night every night for a day or days at a time. This is because our job requieres us to come in and out of the base; but given our previous schedules 8 of us might coincide the same night. What I want to know is: In any given month, how many people can coincide the same night as max, given the following constants:
-there are 6 operations to run daily, which requires a crew of two.
-31 is a group within a bigger group which totals 121 (31 included)
-Usually, those 31 have a 20 day duty pattern which takes them away from the base for at least 3 days at a time, some times more, like 4 or 6 days.
-Before and after every pattern the need to occupy the place for at least one night.
I know that you guys might need more information, if so please let me know I'll answer as accurately as I can.
Thank you in advance for your attention

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: what are the odds? ( probabilities )

What I want to know is: In any given month, how many people can coincide the same night as max, given the following constants

Do you mean: How many people can be working conconcurrently so that there are no more than 6 per night sharing the place?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Landlord

Member

Registered: 2008-07-29

Posts: 1

Re: what are the odds? ( probabilities )

sounds like a good start. Let's also try with a max of 8. Thank you