Question

If ²⁰C_{r + 1} = ²⁰C_{r − 1} , then r is equal to
(a) 10
(b) 11
(c) 19
(d) 12

Answer 1

(a) 10
$r+1+r-1=20$ [∵${}^n{C}_x{=}^n{C}_y\Rightarrow n=x+y\mathrm{or}x=y$]
$$\begin{gathered} \Rightarrow 2r=20 \\ \Rightarrow r=10 \end{gathered}$$