How do you combine cases and sub equations?

My code is:

\begin{numcases}{ P(X_1=x_1,...,X_K=x_)=}
\frac{N!}{x_1!...x_k!}p_1^{x_1}p_2^{x_2}...p_k^{x_k},& \text{when} \sum_{i=1}^kx_i=N
\label{multinomial}
\\
0 & \text{otherwise,} \label{negative}
\end{numcases}

which results in

Is there any way of having equations 3.6a and 3.6b instead of 3.6 and 3.7?

Use subnumcases: (See texdoc cases for full documentation)

\documentclass{article}
\usepackage{amsmath}
\usepackage{cases}
\begin{document}
\begin{subnumcases}{ P(X_1=x_1,\dots,X_K=x_K)=\label{eq}}
\frac{N!}{x_1!\dotsm x_k!}p_1^{x_1}p_2^{x_2}\dotsm p_k^{x_k},& when $\sum_{i=1}^kx_i=N$ \label{multinomial}\\
0 & otherwise, \label{negative}
\end{subnumcases}
\eqref{multinomial} and \eqref{negative} are part of \eqref{eq}.
\end{document}

• +1. Do please replace the first instance of ... with \dots and the second and third instances with \dotsb (or \cdots). – Mico Apr 4 at 9:54
• @Mico Thank you. Done (With \dotsm instead of \dotsb) – Marcel Krüger Apr 4 at 9:57
• @MarcelKrüger how do you reference this equation? – Ng123 Apr 4 at 11:04

You can use the subnumcases environment. Note that the part after & is in text mode, so any formula requires a pair$...$. I also added some improvements: : medsize commands from nccmath for the fractional coefficient and the sum symbol, and smashing the upperpart of the latter for a better symmetry of the brace:

\documentclass{article}
\usepackage{amsmath, nccmath}
\usepackage{cases}

\begin{document}

\begin{subnumcases}{ P(X_1=x_1,\dots,X_K=x_k)=}
\mfrac{N!}{x_1!\dots x_k!}\,p_1^{x_1}p_2^{x_2}\dots p_k^{x_k},& when $\smash[t]{\medop\sum\limits_{i=1}^k}x_i=N$
\label{multinomial}
\\
0 & otherwise, \label{negative}
\end{subnumcases}

\end{document}