A university needs to assign professors to 6 math courses. there are 3 professors available and all of the courses are taught at different times. In how many ways can the professors be assigned to each professor.

A) there are 6 different courses and there are no restrictions on how many courses can be assigned to each professor

should this just be 6!

B) there are 6 different courses and each professor must be assigned exactly 2 classes.

consider the 2 courses as a repeat, we have 6!/(2!2!)

need someone to verify this for me