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📅 March 1, 2026 👤 scraface

Mar 01, 2026

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with indistinguishability within types.
The number of distinct sequences is:
\frac{12!}{5! \cdot 4! \cdot 3!}
$ 12! = 479001600 $
$ 5! = 120 $, $ 4! = 24 $, $ 3! = 6 $
Denominator: $ 120 \cdot 24 \cdot 6 = 120 \cdot 144 = 17280 $
\frac{479001600}{17280} = 27720
Alternatively, step-by-step:
\frac{12!}{5!4!3!} = \binom{12}{5} \cdot \binom{7}{4} \cdot \binom{3}{...
Thus, the number of distinct eating sequences is $ \boxed{27720} $.Que...

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