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Home » Total number of ways to choose 5 samples from 120: - Moon Smoking

Total number of ways to choose 5 samples from 120: - Moon Smoking

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Now, model: we assign types to 4 selected fossils in sequence, with no two ferns adjacent.

📌 We proceed by counting valid type sequences with no two ferns adjacent, then multiply by number of ways to assign actual fossils.

📌 Wait: 1,3: not adjacent, add 4? 3 and 4 adjacent. 1,4: non-adjacent, add 2? 1 and 2 adjacent. 2,4: non-adjacent. Cant add 1 or 3. So maximum 2 ferns.

📌 So possible grams: k = 0, 1, or 2 ferns, with no two Fs adjacent.

📌 Now, for each k, count number of ways to place ferns with no two adjacent, then assign types, then assign actual fossils.

📌 But fossils are distinct, so we must:

📌 Choose positions for ferns: number of ways to choose k non-adjacent positions in 4 slots.

📌 k=2: choose 2 positions, not adjacent.

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