A = {1;2;...;n}
[tex]C_n^2 = 120[/tex]
[tex]C_n^2 = \frac{n!}{2!(n-2)!} = \frac{n(n-1)(n-2)!}{2(n-2)!} = \frac{n(n-1)}{2} [/tex]
[tex] \frac{n(n-1)}{2} = 120[/tex]
[tex]n^2-n-240 = 0 \\ [/tex]
Δ = 1 + 960 = 961
n₁ = [tex] \frac{1+ 31 }{2} [/tex] = 16 ∈ IN
n₂ = [tex] \frac{1- 31 }{2} [/tex] = -15 ∉ IN
n∈{16}
