There are 12 identical balls and 5 distinct containers: A, B, C, D and E. In a random experiment, the 12 balls are randomly put into the 5 containers, with at least one ball in container A but no...

There are 12 identical balls and 5 distinct containers: A, B, C, D and E. In a random experiment, the 12 balls are randomly put into the 5 containers, with at least one ball in container A but no restrictions on the number of balls in the other containers. Let X be the number of empty containers at the end of the experiment. Find its probability distribution function and the expected number of empty containers. Note: Here we assume that every configuration is equally probable