Question

Coroana celui care o rezolva

Answer 1

$C_{n}^{n-2} = 30\\ \\ C_{n}^{n-(n-2)} = 30 \\ \\C_n^2 = 30 \\ \\\dfrac{n!}{2!(n-2)! = 30} \\ \\ \dfrac{(n-2)!(n-1)n}{2!(n-2)!} = 30\\ \\ \dfrac{(n-1)n}{2} = 30 \\ \\ (n-1)n = 60\\ \\ 7\cdot 8 = 56 \\ 8\cdot 9 = 72 \\ \\ \Rightarrow n\notin \mathbb{N} \Rightarrow \boxed{n\in \emptyset}$