xcolor's rowcolor blocking multi-line brackets

Question

I am trying to make a table with different colors alternating per row, and I found that my document was compiling like this:

I've had similar issues with matrices and other large braces, but not others like integrals and sums. I've looked at the solutions on here and here, but I'm not sure that I understand either one, or how it's relevant to my problem.

My questions is whether or not this is an issue with the way I am coloring coloring the rows, and if there was a more conventional way to do so.

My markup is here:

\documentclass{article}
\usepackage[table]{xcolor}
\usepackage{amsmath}
\begin{document}

\begin{table}[h]

\renewcommand{\arraystretch}{1.5}%
\rowcolors{2}{}{gray!10} 
\begin{tabular}{p{3cm}|p{5cm}}

    \textbf{Problem} & \\
    With Color & $n! = 
    \begin{cases} 
        1 & \text{if } n = 0 \\
        (n-1)! &  \text{otherwise}
    \end{cases}$ \\

    Without Color & $n! = 
    \begin{cases} 
        1 & \text{if } n = 0 \\
        (n-1)! &  \text{otherwise}
    \end{cases}$ \\

\end{tabular}
\end{table}
\end{document}

Answer 1

it works with \left\{\begin{array}{rl} ... \end{array}\right. maybe it will help you:

\documentclass{article}
\usepackage[table]{xcolor}
\usepackage{amsmath}
\usepackage{array,cellspace}
\setlength\cellspacetoplimit{4pt}
\setlength\cellspacebottomlimit{4pt}

\begin{document}
    \begin{table}[h]
\renewcommand{\arraystretch}{1.5}%
\rowcolors{2}{}{gray!10}
\begin{tabular}{p{3cm}|>{$}S{p{5cm}}<{$}}
\textbf{Problem}    & \\
        With Color  & n! = \left\{\begin{array}{rl}
                            1       & \text{if } n = 0 \\[-1ex]
                            (n-1)!  &  \text{otherwise}
                            \end{array}\right. \\
    Without Color   & n! = \begin{cases}
                            1       & \text{if } n = 0 \\
                            (n-1)!  &  \text{otherwise}
                            \end{cases} 
\end{tabular}
    \end{table}
\end{document}

Answer 2

Load mathtools in the place of amsmath (mathtools is an extension of amsmath) and use, say, the `dcases* environment:

\documentclass{article}
\usepackage[table]{xcolor}
\usepackage{mathtools}
\begin{document}

\begin{table}[h]
\renewcommand{\arraystretch}{1.5}%
\rowcolors{2}{}{gray!10}
\begin{tabular}{p{3cm}|p{5cm}}
    \textbf{Problem} & \\
    With Color & $n! =
    \begin{dcases*}
        1 & if $ n = 0 $ \\
        (n-1)! & otherwise
    \end{dcases*}$ \\
\end{tabular}
\end{table}

\end{document} 

Answer 3

The environment {NiceTabular} of nicematrix provides tools similar to those of colortbl but using PGF/Tikz for the drawing.

Using that environment, you have directly what you wish (but you need several compilations since nicematrix uses PGF/Tikz nodes).

\documentclass{article}
\usepackage{amsmath}
\usepackage{nicematrix}
\begin{document}
\begin{table}[h]
\renewcommand{\arraystretch}{1.5}%
\begin{NiceTabular}{p{3cm}|>{\arraybackslash}p{5cm}}%
    [code-before = \rowcolors{2}{}{gray!10}]
    \textbf{Problem} & \
    With Color & $n! = 
    \begin{cases} 
        1 & \text{if } n = 0 \
        (n-1)! &  \text{otherwise}
    \end{cases}$ \
    Without Color & $n! = 
    \begin{cases} 
        1 & \text{if } n = 0 \
        (n-1)! &  \text{otherwise}
    \end{cases}$ \
\end{NiceTabular}
\end{table}
\end{document}