+834 Find the number of ways of choosing three circles below, so that no two circles are next to each other.
+1906 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! :)
