SOLUTION: Find a formula of the number of permutations of the set {1,2,3,,,,n} where none of the numbers are in their natural position if you could help me again please

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Question 984076: Find a formula of the number of permutations of the set {1,2,3,,,,n} where none of the numbers are in their natural position if you could help me again please
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the number of "derangements", or the ways a given 
n-permutation can be rearranged so that every element moves to a new 
position is called n-subfactorial, and is denoted by !n, the 
exclamation mark is before the number instead of after it like 
a regular factorial.

The formula is

%22%21n%22%22%22=%22%22matrix%281%2C6%2Cthe%2C+greatest%2Cinteger%2Cnot%2Cexceeding%2Cn%21%2Fe%29,
where  e = 2.718281828459045235360287471352662497757247093699959574966967...

Edwin