JEE Mains · Maths · STD 11 - 6. permutation and combination
The value of \(\sum_{r=0}^{22}{ }^{22} C_r \cdot{ }^{23} C_r\) is
- A \({ }^{45} C_{22}\)
- B \({ }^{44} C_{22}\)
- C \({ }^{45} C_{21}\)
- D \({ }^{44} C_{21}\)
Answer & Solution
Correct Answer
(A) \({ }^{45} C_{22}\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{l}\sum_{r=0}^{22}{ }^{22} C_{22-r}{ }^{23} C_r \\ { }^{22+23} C_{22}={ }^{45} C_{22}\end{array}\)
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