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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
avatar+92674 
+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 

 

 

cool cool cool

CPhill  Jan 25, 2018
 #2
avatar+94105 
+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
 #3
avatar+92674 
+2

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

 

 

cool cool cool

CPhill  Jan 25, 2018

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