one - the size of the bag is up to the individual carrier.
with the new laws you can only take one carry on, and it must fit into the container with out force at the airport, however you may take a laptop and a carry on, or a purse and a carry on. If you are traeling with a child make sure you take out all of the bottles before you go through the security checkpoint as they need to write the information down and become annoyed if they are in the outside pockets.
two - hand bag and my luaggage