[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Suppose that in the hypergeometric distribution, we let

[math]N[/math] and [math]k[/math] tend to [math]\infty[/math] in such a way that the ratio [math]k/N[/math] approaches a real number [math]p[/math] between 0 and 1. Show that the hypergeometric distribution tends to the binomial distribution with parameters [math]n[/math] and [math]p[/math].