Most allow you 1 carry on and a purse/briefcase. Carry on goes in the overhead and is size restricted. The purse/briefcase must fit under the seat in front of you with your feet. There are size restrictions Also, airline have there own rules and some now are cgarging for carry on so it's best to check with your airline.
It depends on your airline. Most allow 1 checked back + 1 carry on + 1 personal item. For budget airlines you usually pay to check a bag.
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