Hong, the mailperson, delivers 5 letters to five houses. what is the probability she delivers at least one letter correctly?
Count the probability that she delivers all the letters incorrectly. This is the number of derangements of 5, which is 44.
Probability: 1 - 44/120 = 19/30
Read more about derangements here: https://en.wikipedia.org/wiki/Derangement