how many ways can we assign the professors
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
Re: how many ways can we assign the professors
Re: how many ways can we assign the professors
Hello, wopashui!
Quote:
A university needs to assign 3 professors to 6 different math courses.
All of the courses are taught at different times.
In how many ways can the professors be assigned to each professor:
A) if there are no restrictions on how many courses
. . can be assigned to each professor.
I see no vagueness.
It states clearly that all six courses could be assigned to one professor.
Each course has a choice of 3 professors.
The number of ways is: . 
Quote:
B) if each professor must be assigned exactly 2 classes.
This is an "ordered partition" problem.
The number of ways is: . 
Re: how many ways can we assign the professors
should the first part be 6^3 instead, sine we are assigning profs to classes, not classes to profs
Re: how many ways can we assign the professors
Quote:
Originally Posted by
wopashui 
should the first part be 6^3 instead, sine we are assigning profs to classes, not classes to profs
How did I know that you were vague on this question?
is the number of ways to assign each element of a set of three to one element in a set of six.
Doing it that way, each professor is assigned exactly one course.
That means that three courses are left uncovered.
Do you think that is what the question means?
Re: how many ways can we assign the professors
then we can assign the remaining 3 courses again to the three profs, will this work?
Re: how many ways can we assign the professors
Quote:
Originally Posted by
wopashui then we can assign the remaining 3 courses again to the three profs, will this work?
Actually, I was trying to show you that your reading does not work. I should have been clearer. Thinking of this as assigning the professors to the classes in ways means two professors can be assigned to the same class. That is clearly not what the question is about.
Without, any restrictions the answer to part A) is 
.
That is the only way that all six courses have a instructor of record.
Re: how many ways can we assign the professors
Pizza Pizza has 12 different deliveries to make and 3 drivers. In how many ways can the deliveries be made by the 3 drivers so that one driver makes 3 deliveries, another driver makes 5 deliveries, and the third driver makes the remaining deliveries?
this is an example given in class, we have this as 12!/(3!5!4!), so i was thinking we can have 6! for the profs question
Re: how many ways can we assign the professors
Quote:
Originally Posted by
wopashui Pizza Pizza has 12 different deliveries to make and 3 drivers. In how many ways can the deliveries be made by the 3 drivers so that one driver makes 3 deliveries, another driver makes 5 deliveries, and the third driver makes the remaining deliveries?
this is an example given in class, we have this as 12!/(3!5!4!), so i was thinking we can have 6! for the profs question
Well yes if each professor teaches two of those courses:
