Finite Math
posted by Rory on .
A producer wants to put on a variety show on television. Assume that the producer has 9 skits and 6 commercials available. In how many ways can the producer create a television show? We assume that a skit is never repeated, but (unfortunately) commercials can appear any number of times.
Thanks for the help!

I will assume that all 9 skits and all 6 commercials are used.
thinks of it as arranging
SSSSSSSSSCCCCCC
which is 15!/(9!6!) = 5005 
Unfortunately that is not the right answer... It was a really good effort though and I do appreciate you helping.. Any other ideas? This problem is driving me crazy! :)

Since you didn't say how the show is to be arranged,
e.g. show, commercial, show, etc
there is little help I can give you 
That is the only information I know. There is a problem in the book similar to this one and I have that answer perhaps that would help. In the book, the problem is 5 skits and 3 commercials and the answer is 3240. I have no idea how they got that or how to apply it to my question.

i hate this problem and there isn't enough info and this isn't fair

In the book, there are 4 spaces reserved for skits and 3 spaces reserved for commercials.
Since skits cannot be repeated, the 4 spaces for skits are:
5*4*3*2
Since commercials CAN be repeated, the 3 spaces reserved for commercials are:
3*3*3
So how you get the different ways is:
5*4*3*2*3*3*3 = 3240 
My teacher told us to refer to a diagram in our book which looked like this:
_ _ _ _ _ _ _
C S S C S S C
C being the commercials, S being the skits. All I did was follow the diagram. Since commercials can play repetitively, you will keep 6 for all of the C's. Skits, it is assumed, will not be repeated. The diagram then looked like this:
6 9 8 6 7 6 6
C S S C S S C
I multiplied them together and got 653184, which was correct on my homework. If there wasn't a diagram to refer back to, then I don't know how else this could have been completed.