Question

If ¹⁵C_3r = ¹⁵C_{r + 3} , then r is equal to
(a) 5
(b) 4
(c) 3
(d) 2

Answer 1

(c) 3
$3r+r+3=15$ [∵${}^n{C}_x{=}^n{C}_y\Rightarrow n=x+y\mathrm{or}x=y$]
$$\begin{gathered} \Rightarrow 4r+3=15 \\ \Rightarrow 4r=12 \\ \Rightarrow r=3 \end{gathered}$$