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  • 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 ______.<div class=

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 ______.

Option: 1

44


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Derangement of 5 students $$ \begin{aligned} & \mathrm{D}_5=5 !\left(1-\frac{1}{1 !}+\frac{1}{2 !}-\frac{1}{3 !}+\frac{1}{4 !}-\frac{1}{5 !}\right) \\ & =120\left(\frac{1}{2}-\frac{1}{6}+\frac{1}{24}-\frac{1}{120}\right) \\ & =60-20+5-1 \\ & =40+4 \\ & =44 \end{aligned}

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