Question

If ${}^n{C}_r{:}^n{C}_{r+1}{:}^n{C}_{r+2}=3:4:5$, then the value of $2n+3r$ is

• A. $238$
• B. $220$
• C. $203$
• D. $240$

Answer 1

The correct option is A $238$

$\frac{{n_C}_r}{{n_C}_{r+1}}=\frac{3}{4}$

$\frac{r+1}{n-r}=\frac{3}{4}$

$\frac{{n_C}_{r+1}}{{n_C}_{r+2}}=\frac{4}{5}$

$\frac{r+2}{n-r-1}=\frac{4}{5}$

$Onsolvingabovewegetr=26,n=62$

$2n+3r=238$

$\frac{{n_C}_r}{{n_C}_{r+1}}=\frac{3}{4}$

$\frac{r+1}{n-r}=\frac{3}{4}$

$\frac{{n_C}_{r+1}}{{n_C}_{r+2}}=\frac{4}{5}$

$\frac{r+2}{n-r-1}=\frac{4}{5}$

$Onsolvingabovewegetr=26,n=62$

$2n+3r=238$