Question based on combinations

My question is if we are given a list of unique digits then how many different numbers can we form from them which satisfies a condition i.e no digit should be at its original place.!

example, if digits are: $1, 2, 3, 4$ then the req numbers are: $2143, 2341, 2413, 3142, 3412, 3421, 4123, 4312, 4321$ i.e answer is $9$!

• First: in a combinatorics environment, you should never place an exclamation point after a number: that means $9$ factorial, not $9$ with emphasis. Second: these are called derangements. You can find more information on Wikipedia, or by searching on this site. – Nick Peterson Jan 20 '14 at 17:03