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Home » aston at the maui banyan - GetMeFoodie

aston at the maui banyan - GetMeFoodie

📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 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?

📌 We are arranging 3 red pens (R), 5 blue pens (B), and 2 green pens (G), with the condition that no two red pens are adjacent.

📌 First, calculate the total number of non-red pens: $5 + 2 = 7$. These 7 pens (all non-red) can be arranged in:

📌 Once these 7 pens are arranged, there are 8 possible gaps where red pens can be placed (one before the first pen, one between each pair, and one after the last), i.e., $7 + 1 = 8$ gaps.

📌 We must choose 3 of these 8 gaps to place the red pens, ensuring no two are adjacent. The number of ways to choose 3 gaps from 8 is:

📌 Thus, the total number of valid arrangements is:

📌 Question: A linguist is analyzing a 6-letter word composed only of the letters A and B, where no two As are adjacent. How many such words are possible?

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