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Home » Ben 10 Ultimate Alien Showdown – The Epic Alien Clash You Won’t Believe! - AssociationVoting

Ben 10 Ultimate Alien Showdown – The Epic Alien Clash You Won’t Believe! - AssociationVoting

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Each colony produces 0, 1, or 2 with equal chance.

📌 We compute $ P_2(k) $ by considering all ways $ k $ colonies can arise from splitting.

📌 Let $ A $ be the number of colonies at hour 2, and each independently produces 0, 1, or 2 offspring. We want total offspring = 3.

📌 But since $ a $ varies, we must sum over all possible $ a $ such that total offspring sum to 3.

📌 Only way: three produce 0, one produces 3? No — max per colony is 2. So need three 0s and one 3? Impossible. Or one 1 and three 0s? No — only 4 colonies. To sum to 3, possibilities: (1,0,0,0) and permutations.

📌 Thus, the probability that exactly 3 colonies exist after 3 hours is:

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