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 __________ . [2023]

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Solution

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 __________ . [2023]

Ans.
(44)

Dearrangement of 5 students

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

$= 120 (\frac{1}{2} - \frac{1}{6} + \frac{1}{24} - \frac{1}{120}) = 60 - 20 + 5 - 1 = 44$

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