The value of $\displaystyle\sum_{r=0}^{22}{ }^{22} C_r{ }^{23} C_r$ is
- ${ }^{45} C _{24}$
- ${ }^{45} C_{23}$
- ${ }^{44} C _{23}$
- ${ }^{44} C_{22}$
The Correct Option is B
Solution and Explanation
\(\overset{22}{\underset{r=0}\sum} {\,\,} ^{22}C_r. ^{23}C_r \)
\(=\overset{22}{\underset{r=0}\sum} {\,\,} ^{22}C_r. ^{23}C_{23-r} \)
\(={\,\,}^{45}C_{23} \)
Hence, the correct option is (B): \(^{45}C_{23} \)
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Concepts Used:
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