Probability of matching letter with marked envelopes

Question

Seven envelopes are marked with letters A thru G. Seven letters marked with the same letters are given to a blind person for inserting one letter in each envelope. What is the probability that the blind person will screw-up and insert wrong letter in an envelope?.

Answer 1

There are 7 envelopes. Therefore number of ways letters placed in envelopes is 7! = 5040

Only one way the blind person will insert right. Therefore right way probability = 1/5040

Therefore probability of wrong way P(wrong) = 1 - P(right) = 1- 1/5040 = 5039/5040

From wording problem may seem difficult but the solution is simpler than many other

probability computations.