Question by Lê Quốc Trần Anh - Discuss with MathYouLike

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26/07/2018 at 01:46

A city is divided into four regions. The city council has decided that a new city hall, a new school, and a new movie theatre shall be built. The only condition is that the school and the movie theatre must not be in the same region. How many ways these four buildings be built in the city? (Ignore the time of construction)

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Tôn Thất Khắc Trịnh 27/07/2018 at 04:51

The city hall has 4 regions to choose from
The school has 4 regions to choose from
The movie theater has 3 regions to choose from (Because it can't be the same region as the school)
So there are \(4\cdot4\cdot3=48\) ways these buildings can be built...

Wait what? FOUR BUILDINGS? I wonder if that's a typo.
Okay, so IF there are 4 buildings and only 1 condition above, the fourth building will aso have 4 regions to choose from.
That would mean \(4\cdot4\cdot3\cdot4=192\) ways these FOUR buildings can be built.

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