If n≤8 and nCr+1=20 and n−1Cr=10then n is equal to

$\frac{^{n} C_{r + 1}}{^{n - 1} C_{r}} = \frac{20}{10}$

$\begin{aligned} \Rightarrow \frac{n!}{(r + 1)! (n - r - 1)!} \frac{r! (n - r - 1)!}{(n - 1)!} = 2 \\ \Rightarrow \frac{n}{r + 1} = 2 \end{aligned}$

This shows that n is even and $r + 1 = n / 2 {Now.}^{n} C_{n / 2} = 20$ and $n \leq 8$

$\Rightarrow n = 6$

If $n \leq 8 {and}^{n} C_{r + 1} = 20 {and}^{n - 1} C_{r} = 10$
then $n$ is equal to