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Home » did the big beautiful bill pass the senate - Redraw

did the big beautiful bill pass the senate - Redraw

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Let’s try:

📌 We have to place 3 C’s and 3 G’s, no two identical adjacent. Also 2 A’s.

📌 First, place the 3 C’s with no two adjacent. As before, number of ways to choose 3 non-adjacent positions in 8 is $ \binom{8 - 3 + 1}{3} = \binom{6}{3} = 20 $.

📌 But now, the remaining 5 positions must hold 2 A’s and 3 G’s, with no two A’s adjacent and no two G’s adjacent.

📌 But as noted, placing 3 G’s in 5 positions with no two adjacent is only possible if they are in positions with gaps.

📌 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\} $, since $ p_3 \le 8 $, $ q_3 \le 8 - 2 = 6 $, but $ q_1 \ge 1 $, $ q_3 \ge q_2 + 2 \ge 1+2=3 $, $ q_3 \le 3 + 2 = 5 $? Let's see:

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