What Curious Cat said above. That is what people do when they know that they will have many more responses than items to give away (e.g. authors giving away advance review copies, or extra copies of their own books). They announce ahead of time, before the “contest” opens, that the items will be given away by random numbers.
Another way to do it, which at least one author does, is he asks one of his family members to pick a number between 1 and [a big number, bigger than the number of people who will respond], and write it down but keep it secret until the contest is over. He tells his readers what the range is. Everyone who wants the item picks a number and posts a comment or sends a message with their chosen number. The first one to get it, or the one who came the closest once the contest is over, gets the item.