Prove the Following Binomial Relationship $\left( \begin{array} { c } 2 n \\n\end{array} \right) = \sum _ { j = 0 } ^ { n } \left( \begin{array} { l } n \\j\end{array} \right) ^ { 2 }$

Essay

Prove the following binomial relationship: $\left( \begin{array} { c } 2 n \\n\end{array} \right) = \sum _ { j = 0 } ^ { n } \left( \begin{array} { l } n \\j\end{array} \right) ^ { 2 }$ Hint: Consider an urn containing red balls and white balls. Consider the number of ways to select balls from this urn at one time.