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I understand that you have an HP Photosmart Premium Fax All-in-One Printer - C309a. I read that you would like to know if the printer could make copies using the black cartridge only while the color cartridges are empty. I'll be glad to assist you with this question.
The few HP printers that can print using black ink cartridge while the color cartridge is out if ink are the printers which use only two cartridges which are black and tricolor.
The HP printers which use more than two ink cartridges are do no support this concept and all the cartridge must have ink for the printer to print. Even though you would like to print in black only, there should be some amount of ink in the color cartridges as well. If the color cartridges are out of ink then the printer will enter into an error stage. The error will not go away until there is ink in all cartridges.
Hope this answers your question. Let me know. Cheers!