I think if you have a choice, I'd have them do the carpet first. That way, the carpet installers have no chance of marring your new moulding. Plus, I think you DO want a bit of clearance between the baseboard and the floor so that the carpet (if not the carpet strip) can go underneath it. I do not know the "perfect" amount of that clearance, but I'm pretty sure it is >0.

Sure wish I'd spent the extra $ for that laser-guided mitre saw.

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