In your closet you have a choice of three different pairs of jeans, three sweaters and five shirts. How many different outfits are possible if all combinations coordinate?

Question

anonymous · Answer

The questions is do I add the choices together or multiply them?

anonymous · Answer

Well to assemble an outfit you must pick 1 jean, 1 sweater, and 1 shirt. So if you must do 3 different tasks to complete a job (make an outfit) you must multiply the number of different ways you can do each task.

anonymous · Answer

It's 165 combinations possible right? Or did I mess up somewhere?

anonymous · Answer

The only time you add is if you can do a job  by doing one task OR another task. Then you would add the different ways you can do task1 and the different ways you can do task2.  But if you must do task1 AND task2 then you multiply.

anonymous · Answer

That seems like too many.

anonymous · Answer

There are 3 different ways you can pick your jeans.
There are 3 different ways you can pick your sweater.
There are 5 different ways you can pick your shirt.

The number of ways you can pick a jean AND a sweater AND a shirt is:
3 * 3 * 5 = 45

anonymous · Answer

Unless you are suggesting you can have a shirt and no sweater also, or a sweater and no shirt

anonymous · Answer

I assume you must have pants at least ;)

anonymous · Answer

I'm not, but the problem was suggesting that it was an equation using combinations, where as you're using the counting principle. 

~ Good assumption.

anonymous · Answer

Or at least I think you are.

anonymous · Answer

Well I am using combinations:

3C1 * 3C1 * 5C1 = 45

But if you are going to have sweaters and no shirts or shirts and no sweaters too it'd be

3C1 * 3C1 * 5C1 + 3C1 * 3C1 + 3C1 * 5C1 = 69

anonymous · Answer

Assuming you must have at least jeans and either a shirt or a sweater (or both) and not more than one of any kind of thing.

anonymous · Answer

I'm not wearing two pairs of pants.. that's just silly.

anonymous · Answer

Well the sheets I'm given to work out are hardly ever right and barely give any information on how to solve the darn thing, so it could be suggesting that you are wearing two pants at once, would get rather hot if you ask me, but it could happen.

anonymous · Answer

I dunno. Sounds hotter to not be wearing pants ;p

anonymous · Answer

To each his own, I suppose.