Math Is Fun Forum

It has been many days since I last posted. Feeling to post again

Anyway,
            There had been eight men and eight hats. They were so much drunk that they could not recognise their own hats. So they picked them up in a random manner. Now what is the chance that no man will choose his own hat?
            Of Course the first step is to find the factorial of 8 which is equal to the number of ways they can pick up the hats in. But it is such a large number that it would take years to write all of them down?

Can You give me the answer????

I know the answer but I dont know how to derive it. So a help would be nice