Question

Find the value of ${}^n{C}_{r-1}{/}^n{C}_r$.

Answer 1

${}^n{C}_{r-1}{/}^n{C}_r=\frac{n!/\left[\right(r-1)!(n-r-1)!]}{n!/[r!(n-r!\left)\right]}=\frac{(n-r)!r(r-1)!}{(n-r+1)(n-r)!(r-1)!}=\frac{r}{n-r+1}$