An absentminded secretary prepares an envelope for each of f

An absent-minded secretary prepares an envelope for each of five letters to different people. He then randomly puts the letters into the envelopes. Find the probability function for the number of letters that are placed in the correct envelope.

Solution

we know that five letters were introduced randomly into envelopes, and ask us about the probability function for the number of cards that were placed in the correct envelope, because we do not have more information and all the letters were placed randomly, I advise you to use the binomial function, becouse I understand that they want the probability that any card into an envelope, and other non-

P(x)=(5/x)*((1/5)^x)*((4/5)^(n-x))
then probabildad serious success (1/5) and failure (4/5) where x = 1,2,3,4 and 5