Dr$.$ Mike Douvas is opening a new sports clinic and is wondering how to arrange the six different departments of the clinic:

A$.$ Waiting;

B$.$ Reception;

C$.$ Records and staff lounge;

D$.$ Examination;

E$.$ Outpatient surgery; and

F$.$ Physical therapy.

The six marked areas are big enough to handle any of the departments, although Dr$.$ Douvas wants to have Reception near the front door $($for obvious reasons$).$ Areas that share a side are approximately $20$ feet apart, while those that share a corner are $35$ feet apart. The distances between A and $E$ and between B and F are $40$ feet, while the distances between A and $F$ and between $B$ and $E$ are approximately $50$ feet. Dr$.$ Douvas also has estimates of the number of trips made by patients and staff between the various departments each day.

Click the icon to view the map of the clinic.

Click the icon to view the number of interdepartmental trips made per day between different departments.

a$.$ If Dr$.$ Douvas wants Reception assigned to area B$,$ the maximum possible number of arrangements is $120.($Enter your response as a whole number.$)$

b$.$ The total distance of the given layout is $17,375$ feet. $($Enter your response as a whole number.$)$