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Home » But is it divisible by $3$ always — yes. - Anadea

But is it divisible by $3$ always — yes. - Anadea

📅 May 15, 2026 👤 scraface

May 15, 2026

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📝 Recent Posts

We proceed in two steps: first place the 3 A’s such that no two are ad...
Step 1: Place 3 non-adjacent A’s in 8 positions.
To place 3 non-adjacent A’s in 8 positions, we use the combinatorial m...
This is equivalent to placing 3 A’s and 5 non-A’s, with at least one n...
To count the number of ways to place 3 non-adjacent A’s in 8 positions...
We use the stars and bars transformation: if we place 3 A’s with at le...
This is now equivalent to distributing 3 indistinct items (remaining n...
But since the non-A positions (the 5 positions not occupied by A) are...
Alternative ( clearer) approach:
The number of ways to choose 3 non-adjacent positions out of 8 is a kn...

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