I am curious, but, I want a variety of different sims for this to choose from, and I was wondering if I could just create a whole bunch of random sims, (and tweak them to my liking), what sort of number of sims would I need to keep from seeing 40 sims with the last name of Smith? Does it just combine sims in the bin? Or does it use random bits and pieces from them?

Just to clarify, we are talking about the household bin right? SP doesn't make any use of the sim bin (in CAH) at all.

It uses random bits and pieces as well as sometimes outright clones of one binned household sim at a time. I don't think you would get one sim's nose with another sim's chin, if that's what you were concerned about, unless it happened to pick both genetic donors from the bin.

But "random" does mean it could choose the same binned household sim 40 times in a row, just like flipping a coin could possibly give you heads 40 times in a row. While some like the approach you describe, I've had totally unwanted results with the bin options far too many times (okay, honestly twice) as I usually place households in the bin for convenient storage, not to be used as fodder for new immigrants. Instead, I set all of the bin sim and bin sim offspring settings to 0 or False and for good measure disallow all of the binned households by using Immigration Disallow Bin by House. That forces immigrating sims to be created in other ways, that is very distant relatives (off the family tree) of existing sims and totally random new ones.
http://nraas.wikispaces.com/StoryPr...FAQ+Immigration