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

eramsby1O1O May 22, 2024

#1**0 **

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! :)

NotThatSmart May 23, 2024