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Mark 2024-03-25 10:12:54 -07:00
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Intermediate/Combinatorics/main.tex
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@ -201,7 +201,7 @@
Now, derive the \textit{multinomial coefficient} $\binom{n}{k_1,k_2,...,k_m}$. \par Now, derive the \textit{multinomial coefficient} $\binom{n}{k_1,k_2,...,k_m}$. \par
\vspace{1mm} \vspace{1mm}
The multinomial coefficient tells us how many distinct ways there to arrange $n$ objects The multinomial coefficient tells us how many distinct ways there to arrange $n$ objects
of $m$ classes, and where each class $i$ contains $k_i$ identical objects. \par of $m$ classes, where each class $i$ contains $k_i$ identical objects. \par
\hint{ \hint{
In \ref{manyballs}, $n = 5$ and $(k_1, k_2, k_3, k_4) = (8, 3, 6, 4)$. \\ In \ref{manyballs}, $n = 5$ and $(k_1, k_2, k_3, k_4) = (8, 3, 6, 4)$. \\
So, the solution to \ref{manyballs} should be given by the multinomial coefficient $\binom{5}{8,3,6,4}$. So, the solution to \ref{manyballs} should be given by the multinomial coefficient $\binom{5}{8,3,6,4}$.