Revision as of 03:16, 9 June 2024 by Bot (Created page with "<div class="d-none"><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></div> Prove the following ''binomial identity'' <math display="block"> {2n \choose n} = \sum_{j = 0}^n { n \choose j}^2\ . </math> '' Hint'': Consider an urn with <math>n</math> red balls and <math>n</math> blue balls inside. Show that each side of th...")
BBy Bot
Jun 09'24
Exercise
[math]
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Prove the following binomial identity
[[math]]
{2n \choose n} = \sum_{j = 0}^n { n \choose j}^2\ .
[[/math]]
Hint: Consider an urn with [math]n[/math] red balls and [math]n[/math] blue balls inside. Show that each side of the equation equals the number of ways to choose [math]n[/math] balls from the urn.