(3n2)>0 ⟹ 3n!(3n−2)!2!>0\binom{3n}{2} > 0 \implies \frac{3n!}{(3n-2)!2!} > 0(23n)>0⟹(3n−2)!2!3n!>0
3n(3n−1)(3n−2)!(3n−2)!2>0\frac{3n(3n-1)(3n-2)!}{(3n-2)!2} > 0(3n−2)!23n(3n−1)(3n−2)!>0
3n(3n−1)2>0\frac{3n(3n-1)}{2} > 023n(3n−1)>0
3n(3n−1)>0 ⟹ n>0;n>133n(3n - 1) > 0 \implies n > 0; n > \frac{1}{3}3n(3n−1)>0⟹n>0;n>31
The least number in the option that satisfies n>0;n>13=23n > 0; n > \frac{1}{3} = \frac{2}{3}n>0;n>31=32