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Home » But 364.5 < 729 → not possible. - Crosslake

But 364.5 < 729 → not possible. - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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But when counting sequences, we need to assign positions.
Standard multinomial: number of sequences with frequencies (2,1,1,0) i...
\frac{4!}{2!1!1!0!} = 12
For each such frequency pattern, number of ways to assign which word h...
Choose the word with frequency 2: 4 choices
Choose two words from remaining 3 to have frequency 1: $\binom{3}{2} =...
The last word has frequency 0
For each such assignment, number of sequences: $ \frac{4!}{2!1!1!} = 1...
So total favorable: $4 \times 3 \times 12 = 144$ — same as before.
So yes, 144 favorable.

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