a$.$ If there are no restrictions $($constraints$)$ on the assignment of professors to offices, how many alternative assignments are there to evaluate?

$40,320$

$64$

$1,024$

$25,600$

$64,000$

There are an infinite number of possibilities

b$.$ The biology department has sent the following information and requests to the OSCM department:

Offices $1,4,5,$ and $8$ are the only offices with windows.

A must be assigned Office $1.$

D and $E,$ the biology department co$-$chairpeople, must have windows.

$H$ must be directly across the courtyard from $D.$

$A,G,$ and $H$ must be in the same wing.

F must not be next to $D$ or $G$ or directly across from $G.$

How many possible solutions $($assignments of faculty to offices$)$ satisfy all of the stated constraints?

Number to possible solutions