# Combinatorial notation (\choose) not working with \frac

This is one of the reasons why using the `\choose`

method is not the best.

What happens? When `\frac`

is expanded, it looks for two arguments, which in your case are determined to be

```
{200 \choose 11}{ 200 \choose {N-189}}
```

and

```
200 \choose N
```

Then TeX will transform this into the primitive call

```
{\begingroup<first argument>\endgroup\over<second argument>}
```

which in your case is

```
{\begingroup{200 \choose 11}{ 200 \choose {N-189}}\endgroup\over 200 \choose N}
```

which is indeed ambiguous as the error message says: it's like

```
a \over b \over c
```

which is of course invalid.

Do yourself a favor and use

```
\documentclass{article}
\usepackage{amsmath}
\begin{document}
$p_N=\frac{\binom{200}{11} \binom{200}{N-189}}{\binom{200}{N}}$
\end{document}
```

which is clearer and doesn't require extra braces like

```
$p_N= \frac{{200 \choose 11}{ 200 \choose {N-189}}}{{200 \choose N}}$
```

By the way, the braces around `N-189`

are redundant. But, really, use the `amsmath`

method that automatically supplies the internal braces when expanding things to the primitive calls.

I have seen often `\choose`

in MathJaX and if I not remember not good also in Open Office or LibreOffice. For my humble opinion are important to have a full minimal working example to see the mistakes. I use often `$\binom{n}{k}$.`

```
\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb,xcolor}
\begin{document}
\[p_N= \frac{\binom{200}{11}\binom{200}{N}}{\binom{200}{N-189}}\]
\end{document}
```