Probability of Getting your Hat Back
Date: Mon, 09 Oct 1995 16:36:05 -0400 From: chris mcmaken Subject: Hat probability There are 5 people with 5 hats. The hats are put into a box. What is the probability that each person will get his or her hat?
Date: 5/30/96 at 14:32:10 From: Doctor Charles Subject: Re: Hat probability The probability that the first person will get the right hat is 1/5. Now there are four people and four hats so the probability that the second person gets their own hat is 1/4. Similarly for the third and fourth people. Of course, if the first four people all get the correct hat then the last person must get the right hat too as it is the only one left. The total probability of everyone getting his own hat is found by multiplying all these together. That is (1/5)*(1/4)*(1/3)*(1/2)*1 = 1/(5*4*3*2*1) = 1/120. Incidentally, the function that gives n*(n-1)*(n-2)* ... *3*2*1 is called the factorial function and is written n! . In general n! is the number of ways of placing n objects in a row. So if we had n people with n hats then the probability would be 1/(n!). -Doctor Charles, The Math Forum
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