Question

If ${}^n{C}_{r-1}=36,{}^n{C}_r=84and{}^n{C}_{r+1}=126$ then r is

• A. 1
• B. 2
• C. 3
• D. none of these

Answer 1

The correct option is C 3

${}^n{C}_{r-1}=36,{}^n{C}_r=84and{}^n{C}_{r+1}=126$
We know that
$\frac{{}^n{C}_{r-1}}{{}^n{C}_r}=\frac{r}{n-r+1}\therefore \frac{36}{84}=\frac{r}{n-r+1}or\frac{r}{n-r+1}=\frac{3}{7}or3n-10r+3=0Also,\frac{{}^n{C}_r}{{}^n{C}_{r+1}}=\frac{r+1}{n-r}=\frac{84}{126}=\frac{2}{3}or2n-5r-3=0Solving\left(1\right)and\left(2\right),wegetn=9andr=3$