lf `n` things are arranged in a row, the number of a ways they can be deranged so that `r` things occupy wrong places while `(n - r)` things occupy their original places, is

`=text()^nC_(n-r)D_r`

where `D_r=r!(1-1/(1!)+1/(2!)-1/(3!)+.............+(-1)^r1/(r!))`

lf `n` things are arranged in a row, the number of ways they can be deranged so that none of them occupies its original place, is

`=text()^nC_0D_n=n!(1-1/(1!)+1/(2!)-1/(3!)+..............+(-1)^n1/(n!))`