Tonya prepared 4 different letters to be sent to 4 different addresses. for each letter, she prepared an envelop with its correct address. if the 4 letters are to be put into the 4 envelops at random, what is the probability that only 1 letter will be put into the envelop with its correct address?

There are 4! = 24 poosible permutations of the four letters. Let the letters be A, B, C and D. Two permutations will have only letter A in the correct envelope, two more permutations will have only letter B in the correct envelope, two more will have only letter C in the correct envelope and two more will have only letter D in the correct envelope. Therefore 8 out of the 24 possible permutations will have only one letter with the correct address. The required probability is 8/24 = 1/3.