combinat
multinomial
compute the multinomial coefficients
Calling Sequence
Parameters
Description
Examples
multinomial(n, k1, k2, ..., km)
n

a positive integer
k1, k2, ..., km
positive integers whose sum is n
The procedure multinomial(n, k1, k2, ..., km) computes the multinomial coefficient denoted $\left(\begin{array}{c}n\\ \mathrm{k1}\,\mathrm{k2}\,\dots \,\mathrm{km}\end{array}\right)$ equal to $\frac{n}{\mathrm{k1}\!\mathrm{k2}\!\cdots \mathrm{km}\!}$ where it is assumed that $n\=\mathrm{k1}\+\mathrm{k2}\+\cdots \+\mathrm{km}$ . If $n\ne 0$, then it is also assumed that $0<m$; that is, there are at least 2 arguments.
The command with(combinat,multinomial) allows the use of the abbreviated form of this command.
$\mathrm{with}\left(\mathrm{combinat}\,\mathrm{multinomial}\right)$
$\left[{\mathrm{multinomial}}\right]$
$\mathrm{multinomial}\left(8\,2\,6\right)$
${28}$
$\mathrm{binomial}\left(8\,2\right)$
$\mathrm{multinomial}\left(8\,2\,3\,3\right)$
${560}$
See Also
binomial
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