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📅 March 1, 2026 👤 scraface

Mar 01, 2026

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A known approach: use **the principle of first placing the most freque...
Let’s try:
We have to place 3 C’s and 3 G’s, no two identical adjacent. Also 2 A’...
First, place the 3 C’s with no two adjacent. As before, number of ways...
But now, the remaining 5 positions must hold 2 A’s and 3 G’s, with no...
But as noted, placing 3 G’s in 5 positions with no two adjacent is onl...
Let’s compute how many ways to place 3 non-adjacent G’s in 5 positions...
Let the positions be $ p_1 < p_2 < p_3 $, $ p_{i+1} \ge p_i + 2 $.
Set $ q_i = p_i - (i-1) $, then $ q_1 < q_2 < q_3 $ in $ \{1,\dots,3\}...
$ q_3 = p_3 - 2 \le 8 - 2 = 6 $, but with $ q_1 \ge 1 $, $ q_2 \ge q_1...

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