Finding all possible sums given 2 lists, matched one to one

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mishima
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Hi, its been a while since I have thought about this type of math, and I can't really remember how to do this or what its even called. I have two lists of numbers:

A: 8, 8, 9, 10, 7, 8
B: 6, 5, 4, 3, 3, 3

I want to find all the different ways I can add elements from A with elements of B. For instance, just adding them vertically as they are here I could get one combination as:

C: 14, 13, 13, 13, 10, 11

When an element from a list is used, its gone. For example, if I added 10 from A and 6 from B, I can't use 6 again (or vice versa). Can anyone nudge me in the right direction?
 
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The number of ways you can pick an entry in the A list to be added to an entry in the B list is the number of permutations, which is n! This number will be reduced by the fact that many of the sums are the same, which feels like a hard problem to handle.
 
Ok, so 720 possibilities. I could've sworn there was a way to account for repeats but like I said it has been a while since I have touched on this style of thinking. Ultimately I am just trying to make a spreadsheet to crunch it all out.