JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Permutations and Combinations

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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

Answer: 44

Solution

This is a derangement problem. The number of derangements of 5 objects is

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}) = 120 (\frac{60 - 20 + 5 - 1}{120}) = 44

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Integer answer

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