If $\frac{{ }^{n+1} C_{r+1}}{{ }^{n+1} C_r}=\frac{n-r+1}{m}$, then $m=$

Question

Aicharya · Accepted Answer

$\begin{aligned} & \frac{{ }^{n+1} C_{r+1}}{{ }^{n+1} C_r}=\frac{n-r+1}{m} \ & \Rightarrow \frac{\frac{(n+1) !}{(r+1) !(n-r) !}}{\frac{(n+1) !}{r !(n-r+1) !}}=\frac{n-r+1}{m} \ & \Rightarrow \quad \frac{n-r+1}{r+1}=\frac{n-r+1}{m} \Rightarrow m=r+1 \end{aligned}$ Hence, option (c) is correct.

If \(\frac{{ }^{n+1} C_{r+1}}{{ }^{n+1} C_r}=\frac{n-r+1}{m}\), then \(m=\)

Solution