\boxed{12600}

February 22, 2026

$\boxed{12600}$

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Denominator: $6 \cdot 2 \cdot 24 \cdot 1 = 288$
\frac{3628800}{288} = 12600
Thus, the number of possible classification outcomes is:
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:

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