Binomial Theorem Question 1
Question 1 - 24 January - Shift 1
The value $\sum _{r=0}^{22}{ }^{22} C_r{ }^{23} C_r$ is
(1) ${ }^{45} C _{23}$
(2) ${ }^{44} C _{23}$
(3) ${ }^{45} C _{24}$
(4) ${ }^{44} C _{22}$
Show Answer
Answer: (1)
Solution:
Formula: Properties of Binomial Theorem for Positive Integer
$ \begin{aligned} & \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} \end{aligned} $
