In an examination, 5 students have been allotted their seats as per...

$5$ boys with allotted roll numbers and seat numbers are seated in such a way that no one sits on the allotted seats. The number of ways of such seating arrangement is equal to the derangement of $5$ boys i.e.,

$= 5 ! \left(1 - \dfrac{1}{1 !} + \dfrac{1}{2 !} - \dfrac{1}{3 !} + \dfrac{1}{4 !} - \dfrac{1}{5 !}\right)$

$= 5 ! - 5 ! + 60 - 20 + 5 - 1$

$= 44$