# Is there a command to write the form of a combination or permutation?

I'm trying to write

^nP_k=\frac{n!}{(n-k)!}
\binom nk=^nC_k=\frac{n!}{k!(n-k)!}


but when compiled the n is a little far away from the P and C for my liking. Is there a command to write this? I know there is a \binom so I was hopeful. If not, is there a way to force the n to be closer?

\documentclass{article}
\begin{document}
$^nP_k=\frac{n!}{(n-k}!} - permutation \\ \binom nk=^nC_k=\frac{n!}{k!(n-k)!} - combination$
end{document}

• \binom is in package amsmath – PatrickT Jan 26 at 8:20

You could use the \prescript command from the mathtools package and define two commands; something along the following lines:

\documentclass{article}
\usepackage{mathtools}

\newcommand\Myperm[^n]{\prescript{#1\mkern-2.5mu}{}P_{#2}}
\newcommand\Mycomb[^n]{\prescript{#1\mkern-0.5mu}{}C_{#2}}

\begin{document}

$\Myperm{k} = \frac{n!}{(n-k)!}\quad \Mycomb{k} = \frac{n!}{k!(n-k)!}\quad \Myperm[m]{k} = \frac{m!}{(m-k)!}\quad \Mycomb[m]{k} = \frac{m!}{k!(m-k)!}\quad$

\end{document} • It's not on topic, I've just noticed \qquad a few times and wondered what it is? – DannyBland Apr 6 '13 at 0:55
• @DannyBland \qquad introduces (both in text and in math mode) a space equal to twice \quad. – Gonzalo Medina Apr 6 '13 at 0:57
• If you want to write \Myperm{x}{y} instead of \Myperm[x]{y} (different brackets) and are okay not having n as the default first parameter, remove[n] from both the \newcommand lines. – Gordon Gustafson Sep 4 '14 at 20:01

You can define your own: ## Code:

\documentclass{article}
\usepackage{amsmath}

\newcommand*{\Perm}{{}^{#1}\!P_{#2}}%
\newcommand*{\Comb}{{}^{#1}C_{#2}}%

\begin{document}
$\Perm{n}{k}=\frac{n!}{(n-k)!}$ - permutation

$\binom nk=\Comb{n}{k}=\frac{n!}{k!(n-k)!}$ - combination
\end{document}


I provide a generic \permcomb macro that will be used to setup \perm and \comb.

The spacing is between the prescript and the following character is kerned with the help of \mkern.

The default kerning between the prescript and P is -3mu, and -1mu with C, which can be changed by using the optional argument of all three macros.

## Code

\documentclass{article}
\usepackage{amsmath}
\newcommand*{\permcomb}[0mu]{{{}^{#3}\mkern#1#2_{#4}}}
\newcommand*{\perm}[-3mu]{\permcomb[#1]{P}}
\newcommand*{\comb}[-1mu]{\permcomb[#1]{C}}
\begin{document}
$\perm{n}{k}$

$\comb{n}{k}$

$\permcomb[-3mu]{J}{l}{k}$
\end{document}


## Output 