Re: number of derangements

It isn't possible. What values do you get for and 8! ?

According to Wikipedia, Derangement - Wikipedia, the free encyclopedia, 8!= 40320 while .

Re: number of derangements

Well this is embarrassing...

I had somehow read the value on my calculator as 4320.

Thank you.

Re: number of derangements

Quote:

Originally Posted by

**Yuuki** How is it possible that D

_{8} > 8! ?

8! is the number of all possible permutations of 8 elements, and D

_{8} is the number of permutations such that no element is in its position.

So {set of derangements}

{set of permutations}.

How can there be more derangements than permutations of the same number of elements?

Here is a bit more. Look at the webpage in reply #2.

It is common to use the approximation,

That shows the impossibility.