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Home » GreenEnvelope: The Eco-Friendly Way to Impress Everyone with Zero Waste! - SUpost

GreenEnvelope: The Eco-Friendly Way to Impress Everyone with Zero Waste! - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 \binom{4}{2} = 6, \quad \left(\frac{1}{6}\right)^2 = \frac{1}{36}, \quad \left(\frac{5}{6}\right)^2 = \frac{25}{36}

📌 P(2) = 6 \times \frac{1}{36} \times \frac{25}{36} = \frac{150}{1296} = \frac{25}{216}

📌 Thus, the probability is $\boxed{\dfrac{25}{216}}$

📌 Question: How many distinct words can be formed using all the letters in the word "BIOINFORMATICS" if the letters must be arranged such that all vowels appear consecutively?

📌 Solution: First, identify the vowels and consonants in "BIOINFORMATICS".

📌 Vowels: I, O, I, A, I → 5 vowels (I appears 3 times, O and A once)

📌 Consonants: B, N, F, R, M, T, C, S → 8 consonants (all distinct)

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