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Find the number of ways of choosing three circles below, so that no two circles are next to each other.

 

 May 22, 2024
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First, let's find how many ways we can choose 3 randomly, no restrictions. 

 

Using the glorious formula for combinations, we have \(9 \choose 3\)\(= 84\). This means there are 84 ways to choose 3 circles randomly. 

 

Now, let's see how many DON'T work. 

 

There are 6 rows and columns of 3 circles, and each of these adjacent 3 have 3 ways we can have an inablid combination. 

 

Thus, we have 6*3 = 18. 

 

\(84-18=66\). There are 66 ways we can do this!

 

I'm not really sure if this is correct...

 

Thanks! :)

 May 23, 2024

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