$1)\backslash ([\backslash$mathbf$\{15\}\backslash )$ points $\backslash (]\backslash )$ An organization has been assigned the prefix $202\mathrm{.}14\mathrm{.}208\mathrm{.}0/22,$ it wants to form subnets for six departments, with the number of hosts as follows:

A: $100$ hosts; B: $60$ hosts; C: $120$ hosts; D: $215$ hosts; E: $30$ hosts; F:$250$ hosts

$($a$)$ Give a possible subnet address for each department. A subnet address should be in the format of $\backslash (\backslash$mathrm$\{$x$.$x$.$x$.$x$/$x$\}\backslash ),$ where $\text{'}\backslash ($ x $\backslash )\text{'}$ is a positive integer. $(12$ points$)$

$($b$)$ If one of the seven departments requires $1,250$ hosts and the rest of the departments do not change their demands on the numbers of hosts, does there still exist a feasible plan for the organization with the prefix $202\mathrm{.}14\mathrm{.}208\mathrm{.}0/22$ to allocate IP addresses to these six subnets? Justify your answer. $(3$ points$)$