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.

Question

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.

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The Answer of 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.

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

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