Question

If ^{n + 1}C₃ = 2 · ⁿC₂ , then n =
(a) 3
(b) 4
(c) 5
(d) 6

Answer 1

(c) 5
$$\begin{gathered} {}^{n+1}C_3=2\times {}^{n}C_2 \\ \Rightarrow \frac{\left(n+1\right)!}{3!\left(n-2\right)!}=2\times \frac{n!}{2!\left(n-2\right)!} \\ \Rightarrow \frac{\left(n+1\right)n!}{3\times 2!\left(n-2\right)!}=2\times \frac{n!}{2!\left(n-2\right)!} \\ \Rightarrow n+1=6 \\ \Rightarrow n=5 \end{gathered}$$