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II-A Winter 2020-21 homework problem
II-A Winter 2020-21 Week 2, homework problem: 2.26.
Suppose you have a group of officers, who each command sergeants (no overlap). Further, each sergeant commands (no overlap) a set of soldiers. (Therefore, each officer is indirectly in command of soldiers.) A team is formed, consisting of soldiers and a command unit. The command unit is either just officers or just sergeants. The soldiers 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.
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!