Question: If $n + 1C_{3} = 2^{n} ⥂ C_{2}$, then n =...

Question

If $n + 1C_{3} = 2^{n} ⥂ C_{2}$ , then n =

Answer 1

$n + 1C_{3} = 2.^{n}C_{2}$

⇒ $\frac{(n + 1)!}{3!(n - 2)!} = 2.\frac{n!}{2!(n - 2)!}$ ⇒ $\frac{n + 1}{3.2!} = \frac{2}{2!}$ ⇒ $n + 1 = 6$ ⇒ $n = 5$ .

Question: If \(n + 1C_{3} = 2^{n} ⥂ C_{2}\), then n =...