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Home » \( P(12) = 500 \cdot 2^12/3 = 500 \cdot 2^4 = 500 \cdot 16 = 8000 \). - Veritas Home Health

\( P(12) = 500 \cdot 2^12/3 = 500 \cdot 2^4 = 500 \cdot 16 = 8000 \). - Veritas Home Health

📅 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?

🔥 Popular Posts

Question**: A circle has a circumference of 31.4 cm. Find its area usi...
Circumference formula: \( C = 2\pi r \).
\( 31.4 = 2 imes 3.14 imes r \Rightarrow r = rac{31.4}{6.28} = 5 \)...
Area = \( \pi r^2 = 3.14 imes 5^2 = 3.14 imes 25 = 78.5 \) cmÂ².
The area is 78.5 cmÂ².
Question**: If \( \log_2(x) + \log_2(x - 2) = 3 \), find \( x \).
Combine logs: \( \log_2(x(x - 2)) = 3 \).
So, \( x(x - 2) = 2^3 = 8 \).
\( x^2 - 2x - 8 = 0 \).
Factor: \( (x - 4)(x + 2) = 0 \).

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