Question:
$\sum_{k=0}^{20}\left({ }^{20} \mathrm{C}_{k}\right)^{2}$ is equal to:
Correct Option: , 3
Solution:
$\sum_{\mathrm{k}=0}^{20}{ }^{20} \mathrm{C}_{\mathrm{k}} \cdot{ }^{20} \mathrm{C}_{20-\mathrm{k}}$
sum of suffix is const. so summation will be ${ }^{40} \mathrm{C}_{20}$