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Home » Not helpful. Try factoring as a quadratic in $ x^2 $: - wispro

Not helpful. Try factoring as a quadratic in $ x^2 $: - wispro

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 How many distinct sequences can be formed using the letters A, A, B, C, C, D, such that no two A's are adjacent?

📌 To solve this problem, we first organize the letters without considering the restriction on A's, then apply the adjacency rule.

📌 Arrange the non-A letters:

📌 The non-A letters are B, C, C, D.

📌 The number of distinct arrangements of these letters is calculated by accounting for the repeated C:

📌 \frac{4!}{2!} = \frac{24}{2} = 12

📌 Determine positions for the A's:

📌 Once the non-A letters are arranged, they create 5 possible "gaps" where A's can be placed: one before the first letter, one between each pair of consecutive letters, and one after the last letter.

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Multiply by 1 (no outer u): $ \frac{1}{15625} $
Second integral:
\int_{0.8}^1 30 \cdot \frac{(1 - u)^5}{5} du = 6 \int_{0.8}^1 (1 - u)^...
Let $ w = 1 - u $, $ dw = -du $, limits $ w = 0.2 $ to $ 0 $:
\int_0^{0.2} w^5 dw = 6 \cdot \frac{w^6}{6} \Big|_0^{0.2} = (0.2)^6 =...
Total: $ \frac{1}{15625} + \frac{1}{15625} = \frac{2}{15625} $
Thus, the probability that all 6 vehicles arrive within some 2-minute...
\boxed{\frac{2}{15625}}
Question: A programmer is testing a neural network that generates bina...
Solution: We want the probability that a binary string of length 8 has...

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