# [Tex/LaTex] command to write the form of a combination or permutation?

math-mode

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}


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