Binomial alignment inside align ambient

Question

I am trying to align some equations in the align ambient. Generally you can put the symbold & before the character you want yo align and that is it. But in this case the characters i want to align (binoms) have different widths and they does not align in their center. I would like to have binoms and vertical dots all aligned over a vertical line passing through the center of the characters. I post my code and the image of what i get and an image (made with an image editor) of what i would like to get.

\begin{align*}
&\binom{n}{n_1}&{} \text{sample text}\\
&\binom{n-n_1}{n_2}&{} \text{sample text}\\
&\vdots &{}\\
&\binom{n-n_1-\dots-n_{k-1}}{n_k} &{} \text{sample text}
\end{align*}

Answer 1

You can do that with the eqparbox package, which uses a system of tags for the latex box commands, so that all boxes sharing the same tag have the width of the widest contents.

\documentclass{article}

\usepackage{amsmath}
\usepackage{eqparbox}
\newcommand{\eqmathbox}[2][M]{\eqmakebox[#1]{$\displaystyle#2$}}

\begin{document}

\begin{align*}
&\eqmathbox{\binom{n}{n_1}}&{} \text{sample text}\\
&\eqmathbox{\binom{n-n_1}{n_2}}&{} \text{sample text}\\
&\eqmathbox{\vdots} &{}\\
&\eqmathbox{\binom{n-n_1-\dots-n_{k-1}}{n_k}} &{} \text{sample text}
\end{align*}

\end{document}