help

I think this might be correct......but maybe someone else has a better solution

Call the set of  people  A  B  C  D  E

And call the set of  the pieces of mail A B C D E in that order

Note that there are  5!  different "words" that can be formed by the set  of letters in the first set

But....only one of these,  ABCDE,  matches the second set

So....the probability that they all get the correct pieces of mail is   1 / 120 

Thanks Chris, I believe your answer is correct but I'd like to talk about it a different way.

Let the people form a line and the envelopes are on the table.

The first person has a 1 in 5 chance of selecting the right letter.  (He selects the correct one)

Now there are 4 on the table so the second person has a 1 in 4 chance of getting the right one (He selects the correct one)

Now there are 3on the table so the second person has a 1 in 3 chance of getting the right one (He selects the correct one)

and so on

so 

P(everyone getting the correct letter) = \(\frac{1}{5}\times \frac{1}{4}\times \frac{1}{3}\times \frac{1}{2}\times \frac{1}{1}=\frac{1}{5!}=\frac{1}{120}\)

Yep.....yours makes better sense.....!!!