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II-A Winter 2020-21 homework problem

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II-A Winter 2020-21 homework problem
by Edward Huang - Thursday, December 10, 2020, 10:31 PM

II-A Winter 2020-21 Week 2, homework problem: 2.26.

Suppose you have a group of 33 officers, who each command 33 sergeants (no overlap). Further, each sergeant commands (no overlap) a set of 2020 soldiers. (Therefore, each officer is indirectly in command of 6060 soldiers.) A team is formed, consisting of 4040 soldiers and a command unit. The command unit is either just 22 officers or just 66 sergeants. The 4040soldiers are chosen so that every soldier is commanded (dirrectly or indirectly) someone in the command unit. How many different teams are possible?

I don't understand the question. If the command unit can either just be 2 officers or 6 sergeants, that does not make sense. Each of the officers would need 3 seargants, so you would need 6 sergeants either way. Also, how can their be only 40 soldiers if each sergeant needs to control 20 soldiers. That would mean you need a lot more soldiers.

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Re: II-A Winter 2020-21 homework problem
by Charles Zhang - Friday, December 11, 2020, 7:53 AM
Hey Edward!

Tip #1: Remember how John said to draw a hierarchy with officers at the top.

Tip #2: The "or" part of this is a little strange, but the idea is that the "2 officers" part means that for every officer you choose, you are indirectly choosing 3 sergeants, for a total of 6 sergeants, all of which are under only 2 officers' command.

Tip #3:  The "6 sergeants" part means that you can choose ANY 6 sergeants, regardless whether or not they are under the same 2 officers.

Tip #4:  If you are stuck, try rewatching the lecture at this part!