Posted by **Rory** on Tuesday, February 17, 2009 at 6:51pm.

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!

- Finite Math -
**Reiny**, Tuesday, February 17, 2009 at 9:24pm
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

- Finite Math -
**Rory**, Tuesday, February 17, 2009 at 9:43pm
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! :)

- Finite Math -
**Reiny**, Tuesday, February 17, 2009 at 11:27pm
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

- Finite Math -
**Rory**, Tuesday, February 17, 2009 at 11:40pm
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.

- Finite Math -
**nicole**, Monday, September 13, 2010 at 10:01pm
i hate this problem and there isn't enough info and this isn't fair

- Finite Math -
**Emily**, Tuesday, September 14, 2010 at 9:59pm
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

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