Here is link to FAQ's from Emirates' website on baggage:

http://www.emirates.com/hk/English/h...ry=214913#faq4

Basically rollers of size up to 45 inches linear measured in total (22 x 15 x 8 inches) under 7 kg is permitted, one such bag per pax in econ class, 2 pcs for biz and first class. I was told by HK Emirates sales office that in addition, one computer bag with computer and/or ladies handbag of reasonable size can also be brought on board. My question was, if computer bag contained not a computer but other personal items, would that be OK? Could not get an answer to that question.

For female pax, I suppose they would be permitted one carry on bag plus one computer bag plus one handbag, but who knows?