While making up his schedule for spring semester, Tom complains that he doesn't have very many choices of schedule because of the general education requirements he has to meet. His advisor tells Tom that he has to take one course from each of English $(5$ choices$),$ History $(7$ choices$),$ Math$/$Stats $(5$ choices$),$ Computer Science $(4$ choices$),$ and general Science $(7$ choices$).$ Does Tom have a legitimate gripe?

$($a$)$ If every possible course is available at the time he's registering, how many possible schedules can he choose from $($disregarding when the classes meet$)?$

Tom can choose from $$ possible schedules.

$($b$)$ In an unprecedented effort to make the general education requirements more accessible, the dean of Tom's college $.$ decides to triple the number of acceptable courses in each of those five areas. What effect does this have on the number of possible schedules?

Tom can choose from $$ possible schedules when the number of acceptable courses are tripled. The number of possible schedules is increased by a factor of $$