$1.$ A large banquet hall has many rectangular tables which can be arranged to have $2$ chairs seated at each long side, and $1$ chair along each short side:

Using arrangement A$,$ tables are aligned along their long edges. Three tables set up using arrangement A look as follows:

When tables and chairs are set up using arrangement B$,$ the tables are aligned along their short edges. Three tables with their chairs in arrangement B look as follows:

$($a$)$ Draw a diagram depicting what it would look like to have $5$ tables and chairs set up using arrangement A$.$

$($b$)$ How many chairs can be arranged around $10$ tables set up using arrangement A$?$

$($c$)$ How many chairs are needed for $25$ tables in arrangement B$?$

$($d$)$ If a banquet seated exactly $200$ guests with no empty chairs, which formation could have been used? How many tables were needed?