Derangement
Category : JEE Main & Advanced
Any change in the given order of the things is called a derangement.
If \[n\] things form an arrangement in a row, the number of ways in which they can be deranged so that no one of them occupies its original place is \[n\,!\,\left( 1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+......+{{(-1)}^{n}}.\frac{1}{n\,!} \right)\].
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