What is the ruling on selling merchandise that the seller does not own, but has a sample of it, then buys it after showing it to the customer to deliver it to him with a profit?

A person is not permitted to sell goods that are not in their possession at the time of the contract, due to the Prophet's (peace be upon him) prohibition of selling what one does not own. An exception to this is the salam sale, provided its conditions are met.

As for merely displaying a type of goods and the buyer promising to purchase them, then the seller later buys them and sells them to the buyer, this is permissible and there is no harm in it. It is not a condition that the buyer knows the source of the goods. However, it is not permissible to conclude the sales contract or take a commitment from the buyer while the goods have not yet been acquired.