初中树状图tree中如何将各种组合结果以（A,B)形式简洁实现？

如图，如何简单实现？用child太麻烦了。用tree我不会列结果的坐标形式和小红小明那种。刚学几天，用实例改的，还不怎么懂，请各位大神指教。代码如下：

\documentclass[UTF8]{ctexart}
%\usepackage{amsmath}
%\usepackage{graphicx}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[every node/.style={inner sep=5pt},edge from parent/.style={draw,->,red,very thick},level 1/.style={sibling distance=25mm},
    level 2/.style={sibling distance=5mm}] % 为所有分支设置层间距
\node {开始} [grow'=right]
child {node[yshift=-15mm]{小红} edge from parent[draw=none]}
child {node {A}
    child {node{小明} edge from parent[draw=none]  child {node[xshift=1mm] {结果}}}
    child {node {A} child {node {(A,A)}}}
    child {node {B}  child {node {(A,B)}}}
    child {node {C} child {node {(A,C)}}}
    child {node {D} child {node {(A,D)}}}
}
child {node {B}
    child {node {A}}
    child {node {B}}
    child {node {C}}
    child {node {D}}
}
child {node {C}
    child {node {A}}
    child {node {B}}
    child {node {C}}
    child {node {D}}
}
child {node {D}
    child {node {A}}
    child {node {B}}
    child {node {C}}
    child {node {D}}
};
\end{tikzpicture}    
\end{document}
\documentclass[UTF8]{ctexart}
\usepackage{tikz}
\usetikzlibrary{graphs,graphdrawing,arrows,graphs.standard}
\usegdlibrary{trees,layered}
\begin{document}
    
\tikz \graph [tree layout,grow'=right,level distance=2.5cm,sibling distance=1mm,sibling sep=2pt
,nodes={red,inner sep=5pt,minimum size=5mm}] { { [number nodes, number nodes sep=*]
    开始->[red] {
            A -> {A--这里写结果,B,C,D},
            B -> {A,B,C,D},
            C -> {A,B,C,D},
            D-> {A,B,C,D}, } },
};
\end{document}

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