52 Chapter 4 5 5 5 4 5 1 3 2 2 3 2 1 4. How many permutations of k things with ties are there? Call this num- ber G(k). We have G(2) = 3, G(3) = 13, G(4) = 75, G(5) = 541. The numbers grow rapidly. Can we arrange the usual deck of fifty-two cards so that each consecutive group of four runs over distinct permutations (ties permitted)? We don't know for sure (but we suspect the answer is yes). All of the open questions for ordered sequences are also open for permutations when ties are permitted. We would also like help pic- turing these things. We have tried to draw pictures of formally dressed permutations wearing ties or standing next to people from Thailand with limited success. Our last development of "order matters" returns to practical card tricks. It also opens up many mathematical challenges. We call the topic Products but will explain it as a practical card trick. A deck is tossed out, cut many times, and three people take consecutive cards. The patter goes as follows: "You're doing a wonderful job of concen- trating on your cards but there are too many images coming in. Let's