AP EAMCET · Maths · Permutation Combination
If \(\frac{{ }^{n+1} C_{r+1}}{{ }^{n+1} C_r}=\frac{n-r+1}{m}\), then \(m=\)
- A \(r\)
- B \(r-1\)
- C \(r+1\)
- D \(1-r\)
Answer & Solution
Correct Answer
(C) \(r+1\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \frac{{ }^{n+1} C_{r+1}}{{ }^{n+1} C_r}=\frac{n-r+1}{m} \\ & \Rightarrow \frac{\frac{(n+1) !}{(r+1) !(n-r) !}}{\frac{(n+1) !}{r !(n-r+1) !}}=\frac{n-r+1}{m} \\ & \Rightarrow \quad \frac{n-r+1}{r+1}=\frac{n-r+1}{m} \Rightarrow m=r+1 \end{aligned}\) Hence,…
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