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Home » Now substitute \( x = g(3) = 7 \) into \( T(x) \): - Silent Sales Machine

Now substitute \( x = g(3) = 7 \) into \( T(x) \): - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 5Question: A bioinformatician is aligning sequences from three different species, each contributing exactly 3 unique genetic markers. If the markers within each species are indistinguishable, but markers from different species are distinguishable, how many distinct sequences can be formed by arranging all 9 markers in a line?

📌 Solution: We are arranging 9 genetic markers in a line, where there are 3 indistinguishable markers from species A, 3 from species B, and 3 from species C. Since markers from the same species are indistinguishable, the number of distinct arrangements is given by the multinomial coefficient:

📌 rac{9!}{3! \cdot 3! \cdot 3!} = rac{362880}{6 \cdot 6 \cdot 6} = rac{362880}{216} = 1680

📌 Thus, the number of distinct sequences is $oxed{1680}$.

📌 Question: A meteorologist is analyzing storm patterns over a 7-day period, where each day is classified as either rainy, cloudy, or sunny. If exactly 3 days are rainy, 2 are cloudy, and 2 are sunny, how many different weather sequences are possible?

📌 Solution: We are assigning weather types to 7 days such that 3 are rainy (R), 2 are cloudy (C), and 2 are sunny (S). Since the days are distinct but the types are grouped, the number of distinct sequences is the multinomial coefficient:

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