All Mixed Up

From “The Riddler”:

From Larry Peranich, a rock-solid probability problem:

A geology museum in California has six different rocks sitting in a row on a shelf, with labels on the shelf telling what type of rock each is. An earthquake hits and the rocks all fall off the shelf. A janitor comes in and, wanting to clean the floor, puts the rocks back on the shelf in random order. The probability that the janitor put all six rocks behind their correct labels is 1/6!, or 1/720. But what are the chances that exactly five rocks are in the correct place, exactly four rocks are in the correct place, exactly three rocks are in the correct place, exactly two rocks are in the correct place, exactly one rock is in the correct place, and none of the rocks are in the correct place?