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} $