How many kinds of gifts do four people exchange with each other?

Nine kinds. There are 1 cases where four people receive gifts by themselves, six cases where two people receive gifts by themselves, and four * 2 = eight cases where one person receives gifts by himself. The total * * * is 15 cases, and these four people can have 4 * 3 * 2 * 1 = 24 cases, so if the topic is established, there are 24- 15 = 9 ways for a * * *.