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After going through the examples given in the book, I don't think there is a difference when going from the name to writing the compound. One potential pattern that I found was that the more positive charge was placed first, but I don't think this significantly matters. Ask your TA though just in case.
I don't think the order of the ligands matter as much when writing out the chemical formula. If you're interested, the book tells you to put the ligands in alphabetical order base off their chemical symbols and single element ligands come first before molecular ligands.
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