Solve the inequation: $\;$ $C^{18}_{m-2} > C^{18}_{m}$, $\;$ $m \in N$
$C^{18}_{m-2} > C^{18}_{m}$
i.e. $\;$ $\dfrac{18!}{\left(m - 2\right)! \left(18 - m + 2\right)!} > \dfrac{18!}{m! \left(18 - m\right)!}$
i.e. $\;$ $m! \left(18 - m\right)! > \left(m - 2\right)! \left(20 - m\right)!$
i.e. $\;$ $m \left(m - 1\right) \left(m - 2\right)! \left(18 - m\right)! > \left(m - 2\right)! \left(20 - m\right) \left(19 - m\right) \left(18 - m\right)!$
i.e. $\;$ $m \left(m - 1\right) > \left(20 - m\right) \left(19 - m\right)$
i.e. $\;$ $m^2 - m > 380 - 39m + m^2$
i.e. $\;$ $38m > 380$
i.e. $\;$ $m > 10$
$\because \;$ $m \in M$ $\implies$ $m = \left\{11, 12, 13, 14, 15, 16, 17, 18\right\}$ $\;$ as the total number of elements is $18$.