You are configuring a network with the IP address $192\mathrm{.}168\mathrm{.}1\mathrm{.}13$ and a subnet mask of $255\mathrm{.}255\mathrm{.}255\mathrm{.}128($or $/25$ in CIDR notation$).$ How many host addresses are available in this subnet, and what is the valid range of host addresses?

$128$ host addresses, Valid range: $192\mathrm{.}168\mathrm{.}1\mathrm{.}1$ to $192\mathrm{.}168\mathrm{.}1\mathrm{.}128$

$126$ host addresses, Valid range: $192\mathrm{.}168\mathrm{.}1\mathrm{.}1$ to $192\mathrm{.}168\mathrm{.}1\mathrm{.}126$

$64$ host addresses, Valid range: $192\mathrm{.}168\mathrm{.}1\mathrm{.}0$ to $192\mathrm{.}168\mathrm{.}1\mathrm{.}63$

$254$ host addresses, Valid range: $192\mathrm{.}168\mathrm{.}1\mathrm{.}1$ to $192\mathrm{.}168\mathrm{.}1\mathrm{.}254$