Question

5 boys with allotted roll numbers and seat numbers are seated in such a way that no one sits on the allotted seat. The number of such seating arrangements is?

Answer 1

The correct answer is 44
Number of seating arrangements
$= 5! \left( 1- \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!}\right)$
$= 5! \left(\frac{120-120+60-20+5-1}{120} \right)$
$= 44$