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Q.

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is ________

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answer is 44.

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Detailed Solution

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

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