Will an airline allow a makeup case, laptop case, & carry-on piece?

Want to carry laptop separate from makeup (medium size) case on my trip. Also taking a small rolling duffle for overhead. Both makeup and laptop cases will fit easily under any seat I’m in. But this is 3 pieces. Anyone know if NW will allow this?
Clarification: Makeup bag won’t fit in rolling duffle, and will not have liquids in it larger than 3 oz. Also, computer case is only laptop and access. Can’t fit in rolling duffle either.

From my own expierence, make sure your laptop is out of any carrying case and in the open when you go through the X-Ray or you will get a lot of grief.

my make up case came!!! yaaaaaaaaaay!

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