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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 $9$!

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    $\begingroup$ 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. $\endgroup$ – Nick Peterson Jan 20 '14 at 17:03
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This type of problems are called derangementproblems. The derangement formula can be found here: http://math.illinoisstate.edu/day/courses/old/305/contentderangements.html

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  • $\begingroup$ wonderful! thanks.! $\endgroup$ – user3185786 Jan 20 '14 at 17:08

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