In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways,…

$5$ 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.,

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

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

$=44$