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Home » A sequence is defined by \( a_n = 3n^2 - 2n + 1 \). Find the 5th term. - Veritas Home Health

A sequence is defined by \( a_n = 3n^2 - 2n + 1 \). Find the 5th term. - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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P(2) = \binom{4}{2} \left(\frac{1}{6}\right)^2 \left(\frac{5}{6}\right...
\binom{4}{2} = 6, \quad \left(\frac{1}{6}\right)^2 = \frac{1}{36}, \qu...
So:
P(2) = 6 \times \frac{1}{36} \times \frac{25}{36} = \frac{150}{1296} =...
Thus, the probability is $\boxed{\dfrac{25}{216}}$
Question: How many distinct words can be formed using all the letters...
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)
Treat the block of vowels as a single "super-letter". So we are arrang...

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