If four letters are put into four envelopes, what is the probability of only three letters are into correct envelopes?

Question

If four letters are put into four envelopes at random, what is the probability that only three of the letters are put into the correct envelopes?

Answer 1

1/24
Probability for first correct letter in the right envelop is 1/4, probability of second letter is 1/3, probability of third letter is 1/2, so 1/(4x3x2)=1/24 is the answer