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Home » Ratio of complex burrows = 3/8 - Crosslake

Ratio of complex burrows = 3/8 - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Solution: This is a multinomial permutation problem. The total sequences are given by:

📌 \frac{10!}{4! \cdot 3! \cdot 3!} = \frac{3628800}{24 \cdot 6 \cdot 6} = \frac{3628800}{864} = 4200

📌 The number of unique video sequences is $\boxed{4200}$.

📌 Question: Three insect species are randomly selected from 10 bee species, 6 butterfly species, and 4 moth species. What is the probability that exactly two are bees and one is a butterfly?

📌 Solution: First, compute the total number of ways to choose 3 species: $\binom{20}{3} = 1140$. The number of favorable outcomes is $\binom{10}{2} \cdot \binom{6}{1} = 45 \cdot 6 = 270$. The probability is:

📌 \frac{270}{1140} = \frac{9}{38}

📌 The probability is $\boxed{\dfrac{9}{38}}$.

📌 Question: A circular table has 7 scientists (3 biologists, 2 physicists, 2 chemists). How many seating arrangements are possible if scientists of the same discipline must sit together?

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