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Home » Divide \( x^4 \) by \( x^2 \) to get \( x^2 \). - Appfinity Technologies

Divide \( x^4 \) by \( x^2 \) to get \( x^2 \). - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Thus, the number of possible classification outcomes is:

📌 \boxed{12600}

📌 Question: A home-schooled student is studying permutations of the word "BANANA" and wants to know how many distinct arrangements exist if the three A's are indistinguishable, the two N's are indistinguishable, and the single B is unique, and moreover, the two N's must not be adjacent?

📌 Solution: First, compute the total number of distinct arrangements of "BANANA" without restrictions. The word has 6 letters with repetitions: 3 A's, 2 N's, and 1 B.

📌 Total unrestricted arrangements:

📌 \frac{6!}{3! \cdot 2! \cdot 1!} = \frac{720}{6 \cdot 2} = \frac{720}{12} = 60

📌 Now, subtract the number of arrangements where the two N's are adjacent.

📌 Treat the two adjacent N's as a single block "NN". Then we are arranging the four units: B, A, A, A, NN — a total of 5 units with 3 identical A's.

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