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from new york to orlando by plane - Moon Smoking

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 Solution: The average of three expressions is given by:

📌 To ensure no two monolingual speakers sit next to each other, we first fix the circular arrangement of the 5 multilingual speakers. Since circular arrangements of $n$ people are rotationally equivalent, the number of distinct arrangements of the 5 multilingual speakers is $(5 - 1)! = 4! = 24$.

📌 Since the monolingual speakers are distinguishable, they can be arranged among themselves in $3! = 6$ ways within the selected gaps.

📌 Therefore, the total number of valid seating arrangements is:

📌 Question: A biologist is studying a population of 10 distinct plant species and wants to select 4 for genetic analysis. If exactly two of the selected plants must be from a rare subgroup of 3 species, how many such selections are possible?

📌 We are to choose 4 plant species in total, with exactly 2 coming from a specific subgroup of 3 rare species, and the remaining 2 from the other 7 species.

📌 Multiplying these gives the total number of valid selections:

📌 Question: A home-schooled student has 3 red pens, 5 blue pens, and 2 green pens. In how many distinct ways can she arrange all the pens in a line if no two red pens may be adjacent?

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