Question

If ⁴³C_{r − 6} = ⁴³C_{3r + 1} , then the value of r is
(a) 12
(b) 8
(c) 6
(d) 10
(e) 14

Answer 1

(a) 12

$r-6+3r+1=43$ [∵${}^n{C}_x{=}^n{C}_y\Rightarrow n=x+y\mathrm{or}x=y$]
$$\begin{gathered} \Rightarrow 4r-5=43 \\ \Rightarrow 4r=48 \\ \Rightarrow r=12 \end{gathered}$$