Question

If ${}^{n}Cr-1$ = 36,${}^{n}Cr$ = 84 and ${}^{n}Cr+1$ = 126, then the value of r is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C

3

Here $\frac{{}^n{C}_{r-1}}{{}^n{C}_r}$ = $\frac{36}{84}$ and $\frac{{}^n{C}_r}{{}^n{C}_{r+1}}$ = $\frac{84}{126}$

$\Rightarrow 3n-10r$ = -3 and $4n-10r$ = 6

On solving, we get n = 9, r = 3