an inefficient secretary places 5 different letters into 5 different addressed envolopes at random find the probability that atleast one of the letters will arrive proper destination

Hi

the probability that atleast one of the letter goes in the right envelope = 1- (probability that none of the letters go in the right envelope)
now, total ways = 5! = 120
ways that none of the letters go in the right envelope = 4! = 24
probability that none of the letters go in the right envelope = 24/120 = 1/5
probability that atleast one of the letter goes in the right envelope = 1 - 1/5 = 4/5