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Home » Stop Struggling with Data—Heres Why Datatool is a Total Game-Changer! - Feedz API

Stop Struggling with Data—Heres Why Datatool is a Total Game-Changer! - Feedz API

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Step 1: Arrange the non-moth insects.

📌 We have 3 beetles (B) and 2 flies (F), total 5 insects. Number of distinct arrangements:

📌 Step 2: Place the 2 moths (M) in non-adjacent positions.

📌 In a sequence of 5 non-moths, there are 6 possible gaps (including ends) where moths can be inserted:

📌 We must choose 2 distinct gaps such that they are not adjacent — but since were placing one moth per gap, any two distinct gaps ensure non-adjacency. So number of ways to choose 2 non-adjacent positions from 6 gaps is:

📌 However, since the moths are indistinguishable, we do not multiply — each pair of gaps gives one valid placement.

📌 Wait — correction: if two moths are placed in different gaps, even if those gaps are adjacent (e.g., between positions 2 and 3), the moths will be adjacent in the sequence unless separated by at least one non-moth — but each gap holds at most one moth.

📌 Wait — this overcounts? Lets reconsider.

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