KöMaL 2006 B3889

Here is a magician's trick that I have seen: He asked one of the spectators to choose 5 cards at random from a deck of 52 French cards and hand them to his assistant. (The assistant was a permanent partner of the magician, so they could have talked before.) The assistant looked at the 5 cards, and handed four of them over to the magician one by one. Then the magician, without receiving any further information, named the fifth card. After the trick, the magician tried to convince mathematically minded spectators as follows: ``My assistant showed me four cards, and those four cards may be any four of the deck, therefore the only way he could convey information to me was through the order of the four cards he showed to me. Since, as you know, there are 4!=24 possible orders of four cards, and the fifth card could be any of 52-4=48, exactly 1 bit of information was missing. It is the guessing of this bit that needs a miracle.'' Does the trick really need supernatural powers?