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

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- May 30th 2009, 07:19 PMTommyBoy22Hats off to helpful mathaticians
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 PMSoroban
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 $\displaystyle 5! = 120$ permutations, with only $\displaystyle \tfrac{1}{120}$ chance of them chosing their own names.

Another approach:

The first has a $\displaystyle \tfrac{1}{5}$ chance of getting his name.

The second has a $\displaystyle \tfrac{1}{4}$ chance of getting his name.

The third has a $\displaystyle \tfrac{1}{3}$ chance of getting his name.

. . . and so on.