Question

The value of $\sum _{r=0}^{22}{}^{22}{C}_r{}^{23}{C}_r$ is

• A. ${}^{45}{C}_{24}$
• B. ${}^{45}{C}_{23}$
• C. ${}^{44}{C}_{23}$
• D. ${}^{44}{C}_{22}$

Answer 1

Answer: (B)

$\sum _{r=0}^{22}{}^{22}{C}_r\cdot {}^{23}{C}_r=\sum _{r=0}^{22}{}^{22}{C}_r\cdot {}^{23}{C}_{23-r}$
$={}^{45}{C}_{23}$