They will pick up one, then put it down and pick up another, and so on, sometimes going back to recheck one, until finally deciding which one to fly off with. They are quick picky.
When the last peanut is gone, sometimes I put out more. And sometimes then I'll see one or two of the jays come back, still carrying the peanuts they had from before. They will put down the old peanut they brought back, and then go through the whole selection process again.