Solution: This problem is a classical concept problem. The total number of sample points in the sample space is

.

　　Event is recorded as "there are no letters in the first two mailboxes" . At this time, two letters are dropped in the last two mailboxes, so the number of sample points included in event is 

,

So

.

　　Event is recorded as "there is only one letter in the first mailbox" . At this time, one of the two letters needs to be put into the first mailbox. There are ways to put it, and the remaining letter needs to be put into the other three. There are ways to put one in a mailbox . According to the multiplication principle , the number of sample points included in event is 

.

So

.