_ k=0 ^ 20 ( ^ 20 C_ k )^ 2 is equal to : - Vidyadip

MCQ

$\sum_{\mathrm{k}=0}^{20}\left({ }^{20} \mathrm{C}_{\mathrm{k}}\right)^{2}$ is equal to :

A
${ }^{40} \mathrm{C}_{21}$
B
${ }^{40} \mathrm{C}_{19}$
✓
${ }^{40} \mathrm{C}_{20}$
D
${ }^{41} \mathrm{C}_{20}$

✓

Answer

Correct option: C.

${ }^{40} \mathrm{C}_{20}$

c
$\sum_{\mathrm{k}=0}^{20}{ }^{20} \mathrm{C}_{\mathrm{k}} \cdot{ }^{20} \mathrm{C}_{20-\mathrm{k}}$

sum of suffix is const. so summation will be ${ }^{40} \mathrm{C}_{20}$

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