# Hats off to helpful mathaticians

• May 30th 2009, 07:19 PM
TommyBoy22
Ok so 5 people place their names in a hat, what is the probability that they will each pull out there own name?
So correct me if i'm wrong (chances are I am) but
there are 5! = 120 permutations, with only 1/120 chance of them chosing their own names
• May 30th 2009, 08:41 PM
Soroban
Hello, TommyBoy22!

Quote:

Ok, so 5 people place their names in a hat.
What is the probability that they will each pull out there own name?

So correct me if i'm wrong (chances are I am) but ...

There are $5! = 120$ permutations, with only $\tfrac{1}{120}$ chance of them chosing their own names.

You are absolutely correct!

Another approach:

The first has a $\tfrac{1}{5}$ chance of getting his name.
The second has a $\tfrac{1}{4}$ chance of getting his name.
The third has a $\tfrac{1}{3}$ chance of getting his name.
. . . and so on.