3
 \begin{inparaenum}[1)]
    \item  number one item
    \item  number two item
    \item  number three item
 \end{inparaenum}

Is it possible to change the color of the number, When I use \textcolor{red}{1)} it is showing red color but it stopped itemizing. So instead of 1,2 3 I just got 1,1,1, for all the items.

4

This works for me:

\begin{inparaenum}[\color{red} 1)]
    \item  number one item
    \item  number two item
    \item  number three item
 \end{inparaenum}
5

You could also use the enumitem package which can now do this as well. In the latest release, the [inline] package options defines three inline lists: enumerate*, itemize*, and description*

\documentclass{article}
\usepackage{xcolor}
\usepackage[inline,shortlabels]{enumitem}
\begin{document}
\begin{enumerate*}[\begingroup\color{red} 1)\endgroup]
    \item  number one item
    \item  number two item
    \item  number three item
 \end{enumerate*}
\end{document}

I used the [shortlabels] package option above to simplify the comparison, but enumitem really offers a lot more flexibility. Related questions:

  1. What are the differences between using paralist vs. enumitem
  2. Suggestions for transitioning from paralist to enumitem package

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