There are five unmarked envelopes on a table, each with a letter for a different person. If the mail is randomly distributed to these five people, with each person getting one letter, what is the probability that everyone gets the correct piece of mail?

SmartMathMan
Jan 24, 2018

#1**+4 **

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

CPhill
Jan 25, 2018

#2**+3 **

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) = \(\frac{1}{5}\times \frac{1}{4}\times \frac{1}{3}\times \frac{1}{2}\times \frac{1}{1}=\frac{1}{5!}=\frac{1}{120}\)

Melody
Jan 25, 2018